Let \(f(x)\) be a differentiable function defined on \([0,2]\) such that \({f}^{'}(x)={f}^{'}(2-x)\) for all \(x\in (0,2…

Let \(f(x)\) be a differentiable function defined on \([0,2]\) such that \({f}^{'}(x)={f}^{'}(2-x)\) for all \(x\in (0,2),f(0)=1\) and \(f\left(2\right)={e}^{2}\). Then the value of \( \int_0^2 f(x) d x\) is

[JEE Main 2021, 24 Feb (Shift 2)]