I need help solving an integral expression.

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I need help solving this problem. I know that: $$\int_{t_1}^{t_0}F(t)\space dt=\frac{t_0^2+t_1^2}{2t_0^2}$$ and I want to find F(t). I tried taking the derivative of $\frac{t_0^2+t_1^2}{2t_0^2}$,but that didn't result in the needed expression when I re-integrated it. Can someone show me how to find $F(t)$?