Finding the area between two curves (or lines).

1. The Area Between Curves
Hamilton Pool, Aug 2007 by
flickr user David A G Wilson

2. Find the total area enclosed between the graph of ƒ(x) and the x-axis.

4. The Fundamental Theorem of Calculus ... part I
Let the function ƒ be continuous on [a, b] with derivative ƒ'. Then ...
Total change in ƒ
In words: Integrating a rate of change function ƒ' over an interval [a, b]
gives the total change in ƒ, ƒ(b) - ƒ(a), over the same interval.
In other words, the integral of a derivative is the same thing as
the total change in it's parent function over the same interval.