Let $\displaystyle G(x)=\int^{2x}_{3x}\;f(t)\:dt$, where $\displaystyle f(t)=\int^{2-t}_{2t-5}\sqrt{1+u^4}\;du$. Then $\displaystyle G''(1)=$
Indeed, what do you do now?
At the risk of sounding arrogant, I would have thought it was reasonably obvious that now you get expressions for f(2x) and f(3x) using the given rule $\displaystyle f(t)=\int^{2-t}_{2t-5}\sqrt{1+u^4}\;du$.
Then you construct the expression 2f(2x) - 3f(3x). Then you differentiate it.