Let f : R → R be defined as f(x) = e^(-x) sin x. If F : [0, 1] → R is a differentiable function such that F(x) = ∫ f(t) dt, x ∈ (x, 0)

Question

Let f : R → R be defined as f(x) = e^–x sinx. If F : [0, 1] → R is a differentiable function such that F(x) = \(\int\limits_0^x\)f(t) dt , then the value of
\(\int\limits_0^1(F'(x) + f(x))e^xdx\) lies in the interval

(1) \(\bigg[\frac{327}{360},\frac{329}{360}\bigg]\)

(2) \(\bigg[\frac{330}{360},\frac{331}{360}\bigg]\)

(3) \(\bigg[\frac{331}{360},\frac{334}{360}\bigg]\)

(4) \(\bigg[\frac{335}{360},\frac{336}{360}\bigg]\)

Answer 1

Answer is (2)