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

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

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