  We generalise the Fundamental Theorem of Calculus to higher dimensions. Our
generalisation is based on the observation that the antiderivative of a
function of $n$-variables is a solution of a partial differential equation of
order $n$ generalising the classical case. The generalised Fundamental Theorem
of Calculus then states that the $n$-dimensional integrals over $n$-dimensional
axis-parallel rectangular hypercuboids is given by a combinatorial formula
evaluating the antiderivative on the vertices of the hypercuboid.
