The problem only asks for the variance of a uniform R.V. on the interval [a,b]
in class we found the following:
$ E[X] = \frac{a+b}{2} $
$ E[X^2] = \frac{a^2+ab+b^2}{3} $
Thus using the formula for variance:
$ Var(X) = E[X^2] - (E[X])^2 \! $
One can reduce the equation to your final answer.
