The Monte Carlo method gives some estimators to evaluate the expectation [ILM0001] based on samples from either the true densityfor from some instrumental density. In this paper, we show that the Riemann estimators introduced by Philippe (1997) can be improved by using the importance sampling method. This approach produces a class of Monte Carlo estimators such that the variance is of orderO(n−2). The choice of an optimal estimator among this class is discussed. Some simulations illustrate the improvement brought by this method. Moreover, we give a criterion to assess the convergence of our optimal estimator to the integral of interest.