If $f(a + b - x) = f(x)$, then $\int_a^b x f(x) dx$ is equal to :

Question

( A ) $\frac{a+b}{2} \int_a^b f(a+b+x) dx$
( B ) $\frac{a+b}{2} \int_a^b f(x) dx$
( C ) $\frac{a+b}{2} \int_a^b f(b-x) dx$
( D ) $\frac{b-a}{2} \int_a^b f(x) dx$