calculus – Give an example of a function that is solution of $y’=f(x)$ and you can’t express it as $ y=int_{a}^{x}f(s)ds$


Give an example of a function that is solution $y’=f(x)$ and you can’t express it as $ y=int_{a}^{x}f(s)ds$

This is a question that my ODE’s theory professor asked to us and he said that the “trick” is to find a proper domain and a proper function such that the funcion has derivative on that domain but the derivative is not an integrable function.

My professor said that the purpose is to show the reason why the fundamental theorem of calculus asks for the integrability of the derivative function.