While the "area beneath a graph", for a graph that is always above the x-axis is the integral itself, that is NOT the "area between the graph and the x-axis" for a graph that is both above and below the x-axis. The area between a graph, y= f(x), and the x-axis is since area is always positive.

This graph is below the x-axis for -3< x< -2, above the x-axis for -3< x< 0 and below the x-axis again for x> 0. To get the total area between it and the x-axis, you need to do it in three parts. For -3< x< 2, the area is . For -2< x< 0, the area is . For 0< x< 2, the area is . The total area is the sum of those three integrals.