A definite integral is the exact area under a curve. A Riemann sum estimates that area with n rectangles. Here f(x) = x^2 on [0, 3], whose exact area is 9. Drag the number of rectangles and the sample point (0 = left edge, 0.5 = midpoint, 1 = right edge) and watch the estimate close in on 9 - the midpoint rule converges fastest, and more rectangles always help.
This is a fixed demonstration concept (NOVA's interactive-visual study modality); the per-misconception, per-course generated version is the frontier work that follows.