Approximate an integral

Question

In a physics textbook, I came across the integral $$I(r_1,r_0)=\int_{r_0}^{r_1}\frac{1}{1-2m/r}\left[1-\frac{r_0^2(1-2m/r)}{r^2(1-2m/r_0)}\right]^{-1/2}dr$$ The author said that the integrand can be expanded to first order in $m/r$ (since here $r_1>r_0\gg m$) to obtain $$I(r_1,r_0)\simeq\int_{r_0}^{r_1}\frac{r}{r^2-r_0^2}\left[1+\frac{2m}{r}+\frac{mr_0}{r(r+r_0)}\right]dr.$$ How to do that? I have really no idea how he came up with that second integral.