If \( f(a+b-x)=f(x) \) then \( \int_{a}^{b} x f(x) d x \) is equal ...

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If \( f(a+b-x)=f(x) \) then \( \int_{a}^{b} x f(x) d x \) is equal to
\( \mathrm{P} \)
(A) \( \frac{a-b}{2} \int_{a}^{b} f(x) d x \)
(B) \( \left(\frac{a+b}{2}\right) \int_{a}^{b} f(x) d x \)
(C) 0
(D) none of these
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