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

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If \( f(a+b-x)=f(x) \), then \( \int_{a}^{b} x f(x) d x \) equal to
\( \mathrm{P} \)
W
(1) \( \frac{a+b}{2} \int_{a}^{b} f(b-x) d x \)
(2) \( \frac{a+b}{2} \int_{a}^{b} f(x) d x \)
(3) \( \frac{b-a}{2} \int_{a}^{b} f(x) d x \)
(4) \( \frac{a+b}{2} \int_{a}^{b} f(a+b+x) d x \)
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