Definite Integration

Let \(\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}\) and \(\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}\) be continuous functions. Then the value of the integral \(\int_\limits{\frac{-\pi}{2}}^{\frac{\pi}{2}}[\mathrm{f}(x)+\mathrm{f}(-x)][\mathrm{g}(x)-\mathrm{g}(-x)] \mathrm{d} x\) is