I have the density of a mixed r.v $X$. $$f(x)=\begin{cases} x/2 & 0\leq x <1 \\ 1/4 & x=1 \\1/4 & x=3 \\ 0 & \text{otherwise}, \end{cases}$$
How do I and calculate $P(X=2)$ and $P(X=3)$? I was thinking that $P(X=2)=F_X(2)-F_X(1)$? If this is the case, should I include the probability of the continuos part in $0\leq x <1 $ by integrating or what?