Let b>a and let X-uniform(a,b) . Prove Var(X) = $\displaystyle (a+b)^2/12$

Var(X)= E(X^2)-E(X)^2

$\displaystyle E(X^2)$=integral from a to b of $\displaystyle x^2/(b-a) = (b^3-a^3)/b-a$

I know E(X)= (b-a)/2 so E(X^2) must be wrong as when I subtract I do not get required Var(X).