Choose the correct answers if $f(a+b-x) = f(x)$ , then $\int\limits_a^bx\;f(x)dx$ is equal to

Question

$\begin{array}{1 1} (A)\frac{a+b}{2}\int\limits_a^bf(b-x)\;dx \\ (B)\frac{a+b}{2}\int\limits_a^bf(b+x)\;dx \\ (C)\frac{b-a}{2}\int\limits_a^bf(x)\;dx \\ (D)\frac{a+b}{2}\int\limits_a^bf(x)\;dx\end{array} $