1. The problem asks: If $B = \{x: x \text{ is an integer between } 1 \text{ and } 2\}$, list the members of set $B$. 2. To find the members of $B$, we need to identify all integers $x$ such that $1 < x < 2$. 3. The integers between 1 and 2 are those greater than 1 and less than 2. Since 1 and 2 are consecutive integers, there are no integers strictly between them. 4. Therefore, the set $B$ contains no elements. 5. Hence, $B = \emptyset$ (the empty set).