1. Let $1 \leqslant x \leqslant 3$. Then the sum of the maximum and minimum values of $|x-1|-|x-3|$ is ( ).
(A) 0
(B) 1
(C) 2
(D) 3
1. A.
From the given, we know
$$
|x-1|-|x-3|=(x-1)-(3-x)=2 x-4 \text{, }
$$

its maximum and minimum values are $2$ and $-2$, respectively. Therefore, the required sum is 0.