Definite Integration

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