Need some help with integration

For instance the integral of x^2 is -1/3x^3+C. In getting to the final answer, where does the 1/3 come from?

The same thing for 2x. Where does the 1/2 come from in the calculations to get to the final answer of x^2?

If someone could explain and give a few more examples than I gave that would be very helpful. Thank you