The RiemannSums applet computes a Riemann sum for a given function and displays the sum and the rectangles that define the sum. In choosing the rectangles, it can use: Left endpoint rule, Midpoint rule, Right endpoint rule, Inscribed rectangles, Circumscribed rectangles, or the Trapezoid rule. (Yes, I know that the trapezoid rule is not exactly a Riemann sum.) The methods that use inscribed and circumscribed rectangles are shown in the menu as "~Inscribed" and "~Circumscribed". The "~" here means "approximate," and it's there since the minimum and maximum of a function on an interval is not always computed exactly. Here is the basic form of the applet, with no applet params:
Here is a version configured with some different colors and several loadable examples:
