Mathematics - Differential Equation Question with Solution | TestHub

Let$f:\left[0,2\right]\to R$be a function which is continuous on$\left[0,2\right]$and is differentiable on$\left(0,2\right) f\left(0\right)=1$. Let$F\left(x\right)=\underset{0}{\overset{x^2}{\int }}f\mathrm{ }\left(\sqrt{t}\right)dt$for$x\in \left[0,2\right].$If$F^{\text{'}}\left(x\right)=f^{\text{'}}\left(x\right)$for all$x\in \left(0,2\right),$then$F\left(2\right)$equals