How do I prove that these two iterated integrals are equal?

Question

Here is the problem I am working on:

For all continuous functions g, is this statement correct?

$$\int _0^1\int _0^y\:g\left(x,y\right)dxdy=\int _0^1\int _x^1\:g\left(x,y\right)dydx$$

I can't wrap my head around what the bounds mean, can anybody help?

Answer 1

Notice that the integration is over the region $\{(x,y):0\le x\le y\le1\}$