Squared moves in two correlated markets

Two markets move as standard Brownian motions $W$ and $B$ with correlation $\rho = 0.6$, so $dW\,dB = \rho\,dt$.

(a) Use the Itô product rule to find $E[W_t^2 B_t^2]$, and then $\mathrm{Corr}(W_1^2, B_1^2)$.

(b) A trend follower runs $\int_0^1 W\,dW$ in the first market and $\int_0^1 B\,dB$ in the second. Use the Itô isometry to find the correlation between the two P&Ls. Does running both books diversify more or less than the 0.6 correlation of the markets suggests?