The Maple Student library provides graphical illustrations of approximations to definite integrals using the leftbox , rightbox and middlebox commands. This worksheet first shows (Section A) how to incorporate these commands into an animation to illustrate convergence of sums of rectangular areas to areas under a curve, thus illustrating the Riemann integral for these particular cases. The worksheet next provides additional procedures for the more general situations where the sample point is randomly chosen in each cell of a uniform partition (Section B), and finally where the partitions themselves are randomly generated subject to a bound on the length of the longest subinterval (Section C). The worksheet continues with procedures to illustrate convergence where the definition is via upper and lower sums (Sections D through I).