Find the area of the region enclosed by these graphs and the vertical lines x = 0 and x = 3

f(x)=-x^2+2x+4 g(x)=-x+4

It's clear from

http://www.wolframalpha.com/input/?i=plot+y%3D-x^2%2B2x%2B4%2Cy%3D-x%2B4+

that the area is just the integral of

f(x)-g(x) for 0<=x<=3