Let \( f: R^{+} \rightarrow R \) be a differentiable function satis...

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Let \( f: R^{+} \rightarrow R \) be a differentiable function satisfying \( f(x)=e+(1-x) \ln \left(\frac{x}{e}\right)+\int_{1}^{x} f(t) d t \) for all
\( \mathrm{P} \) \( x \in R^{+} \). Then find the value of definite integral \( e-\int_{0}^{1} f(t) d t \).
\( \mathrm{W} \)
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