To quantify the flow of particles over a heterogeneous area, some models require the integration of a pointwise dispersal function over source and target polygons. This calculation is a non-trivial task and may require a great deal of computing time. In this paper, an efficient and accurate algorithm is presented to integrate general individual dispersal functions between pairs of convex or non-convex polygons. Geometric calculations are performed using standard tools from computational geometry. Numerical integration is then performed either by a grid method or by an adaptive cubature method. The procedure is illustrated with a case study. It is shown that the cubature method is much more efficient than the grid method and that its error estimates are accurate. The algorithm is implemented in a C++ program, Califlopp