How to evaluate this double integral $\int_{0}^{\pi}dx\int_{x}^{\pi} \frac{\sin y}{y} dy$? I was trying to evaluate double integral:
$\int_{0}^{\pi}dx\int_{x}^{\pi} \frac{\sin y}{y} dy$
I don't know what to do, from double integral calculator the answer is $2$.
I checked indefinite integral from it and it is $\operatorname*{Si}(x)+C$.
I tried to do it with polar form, but I get nothing interesting.
How to evaluate such integral?

Switching the order of integration
$$
\int_{0}^{\pi}\mathbb{d}x\int_{x}^{\pi}\mathbb{d}y=\int_{0}^{\pi}\mathbb{d}y\int_{0}^{y}\mathbb{d}x
$$
your integral is then
$$
\int_{0}^{\pi}\mathbb{d}y\int_{0}^{y}\frac{\sin(y)}{y}\mathbb{d}x=\int_{0}^{\pi}\sin(y)\mathbb{d}y=2
$$
