I suppose the given expression inside the integral is as below.
Let f(x) be function inside ONE Integral on the RHS. Then let X= -x.
In the given integral
is anti symmetric function. so its image wrt y axis. So G(x) = - G(-x). Hence, the area under the curve G(x) for x > 0 is equal and opposite to the area under the curve for x < 0.