Suppose I have a bounded region $A \subset \mathbb{R}^n$ and $T$ is a translation on $\mathbb{R}^n$. How do I show taht
$$\int_{A} 1 = \int_{T(A)} 1$$
This looks seemingly intuitive, as the area of $A$ is unchanged. However, how do I show it mathematically?
Also I'm dealing with Riemann integrals here.