Let \( f(x) \) be a function satisfying \( f^{\prime}(x)=f(x) \) with \( f(0)=1 \) and \( g(x) \...

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Let \( f(x) \) be a function satisfying \( f^{\prime}(x)=f(x) \) with \( f(0)=1 \) and \( g(x) \) be the function satisfying \( f(x)+g(x)=x^{2} \). The, value of the integral \( \int_{0}^{1} f(x) g(x) d x \), is
(A) \( \frac{1}{4}(e-7) \)
(B) \( \frac{1}{4}(e-2) \)
(C) \( \frac{1}{2}(e-3) \)
(D) none of these
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