Mathematics

Problem

Let

f: \mathbb{R} \to \mathbb{R}

and

g: \mathbb{R} \to \mathbb{R}

be continuous functions, then the value of

\int_{-\pi/2}^{\pi/2} [f(x) + f(-x)][g(x) - g(-x)]\,dx

is equal to a.

-1

0

1

d. None of these