Atoms $\tfrac14$ at $-1$ and $\tfrac12$ at 2, plus density $\tfrac14$ on $(2,3)$

Let X be a random variable whose cdf is plotted as: $F=0$ for $x<-1$; $F=\frac14$ on $[-1,2)$; a jump to $\frac34$ at $x=2$; then rising linearly to 1 at $x=3$ and constant afterwards. What will be $E(X^3)$?