Integral By Partial Fractions

The following statements outline the steps for evaluating $\int \frac{1}{x^2-1} \, dx$.

I. The denominator of the integrand, $x^2-1$, factors as $(x-1)(x+1)$.
II. The partial fraction decomposition of $\frac{1}{x^2-1}$ is $\frac{1/2}{x-1} - \frac{1/2}{x+1}$.
III. The result of the integration is $\frac{1}{2}\ln\left|\frac{x-1}{x+1}\right| + C$.

Which of the above statements is/are correct?