Gaussian quadrature can be very effective on smooth data that is available at highly specific node locations. A more common situation is that data is equispaced (if not created explicitly for the purpose of such quadrature). The most effective quadrature methods that are then available relate closely to FD approximations. A particularly noteworthy method was introduced by Gregory already in 1670 (predating the descriptions of calculus by Leibniz and Newton). In cases when the function to be integrated happens to be analytic, complex plane FD approximations can be used for highly accurate contour integration. Given the close relation between integrals and equispaced sums, FD-based methods can be very effective also for infinite sums.