diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index e0e499306..fc81554d6 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -38,20 +38,15 @@ jobs:
       - name: Gusto unit-tests
         run: |
           . /home/firedrake/firedrake/bin/activate
-          python $(which firedrake-clean)
+          which firedrake-clean
           python -m pytest -n 12 -v unit-tests
       - name: Gusto integration-tests
         run: |
           . /home/firedrake/firedrake/bin/activate
-          python $(which firedrake-clean)
+          firedrake-clean
           python -m pytest -n 12 -v integration-tests
       - name: Gusto examples
         run: |
           . /home/firedrake/firedrake/bin/activate
-          python $(which firedrake-clean)
+          firedrake-clean
           python -m pytest -n 12 -v examples
-      - name: Lint
-        if: ${{ always() }}
-        run: |
-          . /home/firedrake/firedrake/bin/activate
-          make lint
diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
new file mode 100644
index 000000000..e6bec0821
--- /dev/null
+++ b/.github/workflows/docs.yml
@@ -0,0 +1,57 @@
+name: Check docs build cleanly
+
+on:
+  # Run on pushes to master
+  push:
+    branches:
+      - master
+  # And all pull requests
+  pull_request:
+
+concurrency:
+  # Cancels jobs running if new commits are pushed
+  group: >
+    ${{ github.workflow }}-
+    ${{ github.event.pull_request.number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  build_docs:
+    name: Run doc build
+    # The type of runner that the job will run on
+    runs-on: ubuntu-latest
+    # The docker container to use.
+    container:
+      image: firedrakeproject/firedrake-docdeps:latest
+      options: --user root
+      volumes:
+        - ${{ github.workspace }}:/home/firedrake/output
+    # Steps represent a sequence of tasks that will be executed as
+    # part of the jobs
+    steps:
+      - uses: actions/checkout@v3
+      - name: Install checkedout Gusto
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          python -m pip install -e .
+      - name: Install Read the Docs theme
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          python -m pip install sphinx_rtd_theme
+      - name: Check documentation links
+        if: ${{ github.ref == 'refs/heads/master' }}
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          cd docs
+          make linkcheck
+      - name: Build docs
+        run: |
+          . /home/firedrake/firedrake/bin/activate
+          cd docs
+          make html
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v1
+        with:
+          name: github-pages
+          path: /__w/gusto/gusto/docs/build/html
+          retention-days: 1
diff --git a/.github/workflows/lint.yml b/.github/workflows/lint.yml
new file mode 100644
index 000000000..8c29106e4
--- /dev/null
+++ b/.github/workflows/lint.yml
@@ -0,0 +1,40 @@
+name: Run lint
+
+on:
+  # Push to master or PR
+  push:
+    branches:
+      - master
+  pull_request:
+
+jobs:
+  linter:
+    name: "Run linter"
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+      - name: Setup python
+        uses: actions/setup-python@v4
+        with:
+          python-version: 3.11
+      - name: Setup flake8 annotations
+        uses: rbialon/flake8-annotations@v1
+      - name: Install linter
+        run: |
+          pip install flake8 pylint
+      - name: Lint codebase
+        run: |
+          make lint GITHUB_ACTIONS_FORMATTING=1
+  actionlint:
+    name: "Lint Github actions YAML files"
+    # There's a way to add error formatting so GH actions adds messages to code,
+    # but I can't work out the right number of quotes to get it to work
+    # https://github.com/rhysd/actionlint/blob/main/docs/usage.md
+    # #example-error-annotation-on-github-actions
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+      - name: Check workflow files
+        uses: docker://rhysd/actionlint:latest
+        with:
+          args: -color
diff --git a/Makefile b/Makefile
index f077972cb..4ffd2902f 100644
--- a/Makefile
+++ b/Makefile
@@ -1,14 +1,22 @@
+# Adds file annotations to Github Actions (only useful on CI)
+GITHUB_ACTIONS_FORMATTING=0
+ifeq ($(GITHUB_ACTIONS_FORMATTING), 1)
+	FLAKE8_FORMAT=--format='::error file=%(path)s,line=%(row)d,col=%(col)d,title=%(code)s::%(path)s:%(row)d:%(col)d: %(code)s %(text)s'
+else
+	FLAKE8_FORMAT=
+endif
+
 lint:
 	@echo "    Linting gusto codebase"
-	@python3 -m flake8 gusto
+	@python3 -m flake8 $(FLAKE8_FORMAT) gusto
 	@echo "    Linting gusto examples"
-	@python3 -m flake8 examples
+	@python3 -m flake8 $(FLAKE8_FORMAT) examples
 	@echo "    Linting gusto unit-tests"
-	@python3 -m flake8 unit-tests
+	@python3 -m flake8 $(FLAKE8_FORMAT) unit-tests
 	@echo "    Linting gusto integration-tests"
-	@python3 -m flake8 integration-tests
+	@python3 -m flake8 $(FLAKE8_FORMAT) integration-tests
 	@echo "    Linting gusto plotting scripts"
-	@python3 -m flake8 plotting
+	@python3 -m flake8 $(FLAKE8_FORMAT) plotting
 
 test:
 	@echo "    Running all tests"
@@ -24,4 +32,4 @@ integration_test:
 
 example:
 	@echo "    Running all examples"
-	@python3 -m pytest examples $(PYTEST_ARGS)
\ No newline at end of file
+	@python3 -m pytest examples $(PYTEST_ARGS)
diff --git a/docs/source/conf.py b/docs/source/conf.py
index 642702049..28a7e16a4 100644
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -254,5 +254,5 @@
     'pyop2': ('https://op2.github.io/PyOP2', None),
     'ufl': ('https://fenics.readthedocs.io/projects/ufl/en/latest/', None),
     'h5py': ('http://docs.h5py.org/en/latest/', None),
-    'python':('https://docs.python.org/2.7/', None),
+    'python':('https://docs.python.org/', None),
 }
diff --git a/gusto/__init__.py b/gusto/__init__.py
index c932d6811..d1a210f01 100644
--- a/gusto/__init__.py
+++ b/gusto/__init__.py
@@ -13,6 +13,7 @@
 from gusto.limiters import *                         # noqa
 from gusto.linear_solvers import *                   # noqa
 from gusto.meshes import *                           # noqa
+from gusto.numerical_integrator import *             # noqa
 from gusto.physics import *                          # noqa
 from gusto.preconditioners import *                  # noqa
 from gusto.recovery import *                         # noqa
diff --git a/gusto/numerical_integrator.py b/gusto/numerical_integrator.py
new file mode 100644
index 000000000..d04ab2f2d
--- /dev/null
+++ b/gusto/numerical_integrator.py
@@ -0,0 +1,63 @@
+import numpy as np
+
+
+class NumericalIntegral(object):
+    """
+    A class for numerically evaluating and tabulating some 1D integral.
+    Args:
+        lower_bound(float): lower bound of integral
+        upper_bound(float): upper bound of integral
+        num_points(float): number of points to tabulate integral at
+
+    """
+    def __init__(self, lower_bound, upper_bound, num_points=500):
+
+        # if upper_bound <= lower_bound:
+        #     raise ValueError('lower_bound must be lower than upper_bound')
+        self.x = np.linspace(lower_bound, upper_bound, num_points)
+        self.x_double = np.linspace(lower_bound, upper_bound, 2*num_points-1)
+        self.lower_bound = lower_bound
+        self.upper_bound = upper_bound
+        self.num_points = num_points
+        self.tabulated = False
+
+    def tabulate(self, expression):
+        """
+        Tabulate some integral expression using Simpson's rule.
+        Args:
+            expression (func): a function representing the integrand to be
+                evaluated. should take a numpy array as an argument.
+        """
+
+        self.cumulative = np.zeros_like(self.x)
+        self.interval_areas = np.zeros(len(self.x)-1)
+        # Evaluate expression in advance to make use of numpy optimisation
+        # We evaluate at the tabulation points and the midpoints of the intervals
+        f = expression(self.x_double)
+
+        # Just do Simpson's rule for evaluating area of each interval
+        self.interval_areas = ((self.x[1:] - self.x[:-1]) / 6.0
+                               * (f[2::2] + 4.0 * f[1::2] + f[:-1:2]))
+
+        # Add the interval areas together to create cumulative integral
+        for i in range(self.num_points - 1):
+            self.cumulative[i+1] = self.cumulative[i] + self.interval_areas[i]
+
+        self.tabulated = True
+
+    def evaluate_at(self, points):
+        """
+        Evaluates the integral at some point using linear interpolation.
+        Args:
+            points (float or iter) the point value, or array of point values to
+                evaluate the integral at.
+        Return:
+            returns the numerical approximation of the integral from lower
+            bound to point(s)
+        """
+        # Do linear interpolation from tabulated values
+        if not self.tabulated:
+            raise RuntimeError(
+                'Integral must be tabulated before we can evaluate it at a point')
+
+        return np.interp(points, self.x, self.cumulative)
diff --git a/unit-tests/test_numerical_integrator.py b/unit-tests/test_numerical_integrator.py
new file mode 100644
index 000000000..53d0b1131
--- /dev/null
+++ b/unit-tests/test_numerical_integrator.py
@@ -0,0 +1,34 @@
+"""
+Tests the numerical integrator.
+"""
+from gusto import NumericalIntegral
+from numpy import sin, pi
+import pytest
+
+
+def quadratic(x):
+    return x**2
+
+
+def sine(x):
+    return sin(x)
+
+
+@pytest.mark.parametrize("integrand_name", ["quadratic", "sine"])
+def test_numerical_integrator(integrand_name):
+    if integrand_name == "quadratic":
+        integrand = quadratic
+        upperbound = 3
+        answer = 9
+    elif integrand_name == "sine":
+        integrand = sine
+        upperbound = pi
+        answer = 2
+    else:
+        raise ValueError(f'{integrand_name} integrand not recognised')
+    numerical_integral = NumericalIntegral(0, upperbound)
+    numerical_integral.tabulate(integrand)
+    area = numerical_integral.evaluate_at(upperbound)
+    err_tol = 1e-10
+    assert abs(area-answer) < err_tol, \
+        f'numerical integrator is incorrect for {integrand_name} function'