If \( f(x)=\int_{0}^{1} e^{|t-x|} d t \) where \( (0 \leq x \leq 1) \), then maximum value of \(...

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If \( f(x)=\int_{0}^{1} e^{|t-x|} d t \) where \( (0 \leq x \leq 1) \), then maximum value of \( f(x) \) is
(a) \( e-2 \)
(b) \( e-3 \)
(c) \( e-1 \)
(d) \( 2(\sqrt{e}-1) \)
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