Suppose \( f(x) \) and \( g(x) \) are two continuous functions defi...

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Suppose \( f(x) \) and \( g(x) \) are two continuous functions defined for \( 0 \leq x \leq 2 \).
P
Given \( f(x)=\int_{0}^{1} e^{x+t} \cdot f(t) d t \) and \( g(x)=\int_{0}^{1} e^{x+t} \cdot g(t) d t+x \)
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The value of \( f(1) \) equals :
(a) 0
(b) 1
(c) \( e^{-1} \)
(d) \( e \)
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