posted by 009 .
Evaluate the integral of abs(x) from -4 to 4.
graph f(x). It is just two triangles of base 4, height 4. No integration required.
If you do insist on integrating, recognize that f(x) is a piecewise function, and must be divided at x=0.
f(x) = -x for x<0
f(x) = x for x>=0