Let X be a uniform r.v. over (−1, 1). Let Y = X^2.

Question

I'm having problems solving this problem "Let X be a uniform r.v. over (−1, 1). Let $Y = X^n.$ Calculate: the covariance of X and Y.

I believe that i should use: $$ cov(x,y) = E(x,y) - E(x)E(y)$$ but i don't understand how am i supposed to calculate $E\{x\}$ or $E\{y \}$.

if my logic is correct the statement " Let X be a uniform r.v. over (−1, 1)" could translate to $E\{x\} = \frac{1}{2}$ but then i can't see how to calculate $E\{y \}$. Can someone put me on the right track please?