  We use groupoids and the van Est map to define Riemann sums on compact
manifolds (with boundary), in a coordinate-free way. These Riemann sums
converge to the usual integral after taking a limit over all triangulations of
the manifold. We show that the van Est map determines the n-jet of
antisymmetric n-cochains. We discuss using this Riemann sum construction to put
the Poisson sigma model on a lattice.
