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Let \( f \) be a differentiable function satisfying the relation \( f(x+y)=f(x)+f(y)-2 x y+\left(e^{x}-1\right)\left(e^{y}-1\right) \forall x, y \in R \) and \( f^{\prime}(0)=1 \). \( \{f(2)\} \) is equal to :
(a) \( e^{2}-5 \)
(b) \( e^{2}-6 \)
(c) \( e^{2}-7 \)
(d) \( e^{2}-8 \)
[Note : \( \{y\} \) denotes the fraction part function of \( y \).]
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