JEE Math Practice Question

Let f : R $$ \to $$ R be defined as f(x) = e$$-$$xsinx. If F : [0, 1] $$ \to $$ R is a differentiable function with that F(x) = $$\int_0^x {f(t)dt} $$, then the value of $$\int_0^1 {(F'(x) + f(x)){e^x}dx} $$ lies in the interval

1. A.$$\left[ {{{331} \over {360}},{{334} \over {360}}} \right]$$
2. B.$$\left[ {{{330} \over {360}},{{331} \over {360}}} \right]$$
3. C.$$\left[ {{{335} \over {360}},{{336} \over {360}}} \right]$$
4. D.$$\left[ {{{327} \over {360}},{{329} \over {360}}} \right]$$