Removable Discontinuity and Differentiability

Consider the function $f$ defined by $f(x) = \frac{x^3 - 3x + 2}{x - 1}$. Which of the following statements are true?

I. The function $f$ has a removable discontinuity at $x=1$.

II. The derivative of $f$ at $x=2$ is $5$.

III. The function $f$ is differentiable at $x=1$ because its discontinuity is removable.