If \( \int_{0}^{x} f(t) d t=x+\int_{x}^{1} t f(t) d t \), then the value of \( f(1) \) is (A) \(...

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If \( \int_{0}^{x} f(t) d t=x+\int_{x}^{1} t f(t) d t \), then the value of \( f(1) \) is
(A) \( 1 / 2 \)
(B) 1
(C) \( -1 / 2 \)
(D) undefined
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