If \( x \) and \( y \) are independent variables and \( f(x)=\left(...

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If \( x \) and \( y \) are independent variables and \( f(x)=\left(\int_{0}^{x} e^{x-y} f^{\prime}(y) d y\right)-\left(x^{2}-x+1\right) e^{x} \),
\( \mathrm{P} \)
W where \( f(x) \) is a differentiable function, then \( f\left(\frac{-1}{2}\right) \) equals :
(a) \( 2 \sqrt{e} \)
(b) \( -2 \sqrt{e} \)
(c) \( \frac{-2}{\sqrt{e}} \)
(d) \( \frac{2}{\sqrt{e}} \)
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