Why is the following function discontinuous at $x=1$?

$$f(x) = \begin{cases} \displaystyle \frac{x^2-x}{x^2-1} & \textrm{if }x \neq 1 \\ \\ 1 & \textrm{if }x = 1 \end{cases}$$

(a) $f(1)$ does not exist.
(b) $\displaystyle \lim_{x \to 1} f(x)$ does not exist (or is infinite).
(c) Both (a) and (b).
(d) $f(1)$ and $\displaystyle \lim_{x \to 1} f(x)$ exist, they are not equal.