With this change of variables we can express the integral of Eq. (20) as I=∫bap(y)F(y)p(y)dy=∫˜b˜aF(y(x))p(y(x))dx, meaning that a Monte Carlo evaluation of the above integral gives ∫˜b˜aF(y(x))p(y(x))dx=1NN∑i=1F(y(xi))p(y(xi)).