Let $X$ and $Y$ be two independent random variables, each uniformly distributed on $[-1,1],$ then find $\operatorname{Var}(X+Y).$
My attempt : $$\operatorname{Var}(X+Y) =\operatorname{Var}(X) + \operatorname{Var}(Y) +2\operatorname{Cov}(X,Y) = \operatorname{Var}(X) + \operatorname{Var}(Y) = 2\operatorname{Var}(X) = \frac{2}{3}.$$
But the answer given is $2;$ what am I missing?