Tricky Integral !

Calculus Level 2

if f(x) and g(x) are 2 real valued functions such that : \[f:R \rightarrow R\] \[g:R \rightarrow R\]

then the value of the integral : \[\int_{-\pi/2}^{\pi/2}[(f(x) + f(-x)][g(x) - g(-x)] dx = ? \]