How to find the Area Between Two Curves

Graphed below are the functions f(x) = 2 - x and g(x) = x² - 4. What if we want the area trapped in between. How does this compare with the integrals for f(x) and g(x)

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Click the check boxes to see the area between the two curves and the two integrals.

Jason McCullough, October 7, 2010, Created with GeoGebra