Answer
False
Work Step by Step
As a counterexample, consider the graphs of the functions $y=x$ and $y=x^2$. The graphs intersect at x=0, the midway between x=-1 and x=1.
But, $$\int_{-1}^1x-x^2dx = \left[\frac{x^2}{2}-\frac{x^3}{3}\right]_{-1}^1=-\frac{2}{3}\ne 0 $$
