I need to evaluate $\displaystyle I_y=\int_{\pi}^{2 \pi} \int_0^{\frac{sin^2(x)}{x^2}} y^2 \ dy \ dx=\frac{1}{3} \int_{\pi}^{2 \pi} \frac{sin^6 (x)}{x^6} dx$Find the moment of inertia with respect to the y axis of a thin sheet of constant density $\displaystyle \delta=1$ bounded by the curve $\displaystyle y=\frac{sin^2(x)}{x^2}$ and the interval $\displaystyle \pi \leq x \leq 2 \pi$.

As far as I know, this can't be integrated. This suggests that I have done something wrong with my initial integral.

Can anyone see what it is?