Integrator Applet to find right, left, and general Riemann sum as well as upper and lower sums (part of the Interactive Real Analysis project).
Also check the general introduction to the Riemann integral as well as a discussion of various integration techniques. You may also want to learn more about the Lebesgue integral, a generalization of the Riemann integral.
This "mathlet" has been published in Journal of Online Mathematics and its Applications. Click here for the online reference.