How do i get from this $\displaystyle 1/2\pi*\int_{-\infty}^\infty\ dt \int_{-3\pi}^{3\pi}\ sin(u)sin(tx)sin(tu) du$

to this:

$\displaystyle 2/\pi*\int_{0}^\infty\ dt\int_{0}^{3\pi}\sin(u)sin(tx)sin(tu) du$

How and why does he change the intervals? I can't understand what he did.

Could someone please explain?

It's not multiplied, it's a double integral.