The integral \( \int_{0}^{\pi} x f(\sin x) \mathrm{d} x \) is equal...

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The integral \( \int_{0}^{\pi} x f(\sin x) \mathrm{d} x \) is equal to
(a) \( \frac{\pi}{2} \int_{0}^{\pi} f(\sin x) d x \)
(b) \( \frac{\pi}{4} \int_{0}^{\pi} f(\sin x) d x \)
(c) \( \pi \int_{0}^{\pi / 2} f(\sin x) d x \)
(d) \( \pi \int_{0}^{\pi / 2} f(\cos x) d x \)
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