A distribution function with two jumps and a uniform stretch

Suppose a distribution function $F:\mathbb{R}\to[0,1]$ of a random variable X is as follows:

$$F(x)=\begin{cases} 0, & x<0,\\ 1/4, & 0\le x<1,\\ 1/2, & 1\le x<2,\\ 1/2+(x-2)/2, & 2\le x<3,\\ 1, & x\ge3. \end{cases}$$

Then $E(X)$ is: