Let \(f: R \rightarrow R\) be defined as \(f(x)=e^{-x} \sin x\). If \(F:[0,1] \rightarrow R\) is a differentiable functi…

Let \(f: R \rightarrow R\) be defined as \(f(x)=e^{-x} \sin x\). If \(F:[0,1] \rightarrow R\) is a differentiable function such that \(F(x)=\int_0^x f(t) d t\), then the value of \(\int_0^1\left(F^{\prime}(x)+f(x)\right) e^x d x\) lies in the interval.

[JEE Main 2021, 17 Mar (Shift 2)]