Mathematics - Differential Equation Question with Solution | TestHub

Let$f\left(x\right)$be a differentiable function defined on$\left[0, 2\right]$such that$f^{\text{'}}\left(x\right)=f^{\text{'}}\left(2-x\right)$for all$x\in \left(0,2\right),f\left(0\right)=1$and$f\left(2\right)=e^2.$Then the value of${\int }_0^{2}f\left(x\right)dx$is