Can we calculate the limits of integration of a function whose derivative is given without integrating the derivative function?

Answer 1

I don't understand the question.

If you have a function, you can get the indefinite integral using the standard methods. There will be an unknown "constant of integration", which cannot be known without additional information. If you evaluate the integral over a specific interval, the constant of integration will drop out.

If you know both the function and its definite integral, you cannot necessarily know the integration interval.