Variance of the integral of W against dW

Let $W$ be a standard Brownian motion and $I_T = \int_0^T W_t\,dW_t$ (an Itô integral). Find $E[I_T]$ and $\mathrm{Var}(I_T)$. Do it two ways: with the Itô isometry, and with the closed form for $I_T$.