If $f(y) = e^y,\; g(y) = y; \; y>0$ and $F(t) = \int^t_0 f(t-y) \;g(y) \;dy$, then :

Question

( A ) $F(t) = e^t - (1 + t)$
( B ) $F(t)=1-e^{-t} (1+t)$
( C ) $F(t) = te^{-t}$
( D ) $F(t) = te^t$