JEE Previous Year Question

Let $f\text{:}R\to R$ be defined as $f\left(x\right)=e^{-x}\text{sin}x$. If $F\text{:}\left(0\text{,}1\right)\to R$ is a differentiable function such that $F\left(x\right)=\sum f\left(t\right)\text{dt}$, then the value of $\sum (F^{\text{’}}\left(x\right)+f\left(x\right))e^x\text{dx}$ lies in the interval

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.