For an integral like $\displaystyle \int_{0}^{1}\frac{1dx}{(x+2)^2(x-3)} $

I know the PFD would be written something like $\displaystyle \frac{A}{(x+2)}+\frac{B}{(x+2)^2}+\frac{C}{(x-3)} $

But would that be the same as $\displaystyle \frac{A}{(x+2)^2}+\frac{B}{(x+2)}+\frac{C}{(x-3)} $ ? I was going to type it into a calculator and test, but I thought it might be quicker to ask somebody here.