Riemann Sums

Approximate the area under the curve of a function using Riemann Sums. Choose between upper or lower sums, change the start and end values for x, and change the number of rectangles with the slider for n.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

What is the difference between the upper and lower sums?
Why do they give different values?
Is one more accurate than the other? Why?
How could you get a more accurate approximation?

Jenna Jerez, 24 October 2013, Created with GeoGebra