$f$ is Lebesgue integrable in triangle domain

Suppose $f \in L(T)$, where $T$ is a triangular domain in$\mathbb{R}^2$ with vertices at $(0, 0)$, $(1, 0)$, and $(1, 1)$.Prove that

$$ \int_T f(x,y) \, dx \, dy = \int_0^1 \left( \int_0^x f(x,y) \, dy \right) dx = \int_0^1 \left( \int_y^1 f(x,y) \, dx \right) dy. $$

I currently have no idea how to begin this problem. Could someone shed some light on this problem? Thanks very much!