This last demo effectively summarizes the connection between Upper and Lower Sums. The Upper Sum gives an upper bound on the value for the volume under the function graph, and the Lower Sum gives a lower bound. Increasing the "res" variable, you can see that the difference between the Upper and Lower Sum grows smaller and smaller. This demonstrates that the Upper and Lower Prisms converge to the same volume, and thus the Riemann integral of the volume under a function graph is defined.