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

$$f(x) = \begin{cases} 1+x^2 & \textrm{if }x < 1 \\ \\ 4-x & \textrm{if }x \geq 1 \end{cases}$$

(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.