On page 8 of this paper, it says that there is a closed form of 1-Wasserstein distance on $\mathbb{R}$: for any r.v.s $X,Y$ with CDF $F_X,F_Y$, we have
$$W_1(X,Y)=\int|F_X(t)-F_Y(t)|dt$$
Why is this true? I have no idea how to get this closed-form representation.