1. ## Double integral

I've been given the function:

$f:\mathbb{R}\to\mathbb{R}$ given by $f(x)=\frac{\sin(x)}{x}, x\neq 0$ and $f(x)=0$ otherwise.

Calculate the double integral:

$\int_0^1 \left(\int_y^1f(x)dx\right)dy$

I'm not sure how to tackle this one, any hints?

2. $\int_0^1 \left(\int_y^1 \frac{\sin x}{x} dx \right) dy= \int_0^1 \left(\int_0^x \frac{\sin x}{x} dy\right) dx.$

3. Thanks I was hoping for something like that,

However, I have yet to understand why it's legitimate to take that step

4. It follows by investigating the region of integration.