Chapter 4.2 Summary:
You can find the limit of upper and lower sums when finding a positive area under a function, but the limit as n goes to infinity is the same. Right hand sums are easy and make finding areas under a curve simple. Another thing taught in this section was Reimann Sums. Reimann Sum is equal to the definite integral to the same integral.
4.2a
4.2b
http://www.rootmath.org/calculus/area-intro
Example Problems: 
Calculus Ants 