Do you remember Riemann sums with midpoints, left endpoints, and right endpoints? Those are only three of the many points that can be taken. The sample points can be taken from anywhere.
This Riemann sum starts with 4 midpoints, but you can change each point to anything in its interval. You can also change the number (n) of slices using the slider. Hit the randomize button will randomize the sample points. Once you have done that, you will also be able to fine-tune your estimation with gradient descent.