Welp, Desmos saved the day again with its ability to approximate areas under curves using lower and upper sums and clearly demonstrate that we get closer and closer to the true area the more rectangles we choose to use.
I’ve created an applet which is pretty user friendly with some pretty neat features. You can find it here. A couple neat things to explore is that you can hide/show the upper sum, lower sum, and the actual area by clicking on the folder icons on the left. If you are interested in seeing the upper sum, lower sum, or actual area, you can find it by clicking the triangles next to “Upper Sum”, “Lower Sum”, and “Area”.