If \( I_{1}=\int_{0}^{\pi} x f\left(\sin ^{3} x+\cos ^{2} x\right) d x \) and \( I_{2}=\int_{0}^...

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If \( I_{1}=\int_{0}^{\pi} x f\left(\sin ^{3} x+\cos ^{2} x\right) d x \) and \( I_{2}=\int_{0}^{\pi / 2} f\left(\sin ^{3} x+\cos ^{2} x\right) d x \) then
(A) \( I_{1}=I_{2} \)
(B) \( I_{1}+I_{2}=0 \)
(C) \( I_{1}=2 I_{2} \)
(D) None of these
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