areas between curves (idea)

The area of the region bounded by the curves y=f(x), y=g(x) and the lines x=a and x=b, where f and g are continuous and f(x) => g(x) for all x in [a,b] is:

the integral from a to b of [f(x) -g(x)]dx.

From Calculus: Single Variable Early Transcendentals. By Stewart, 3rd edition.

Think math damn you, math!!