Question: Show that the uniform distribution random variable X with probability density function

\[f\left( x \right)=\left\{ \begin{aligned} & \frac{1}{B-A}\,\,\,\,\,\,\,\,\,\,\,\,\text{if A}\le x\le B \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right.\,\,\,\,\,\]

has expected value

\[E\left( X \right)=\frac{A+B}{2}\]