The line x = 2 cuts R into two parts.

Explanation

1. 01

   For $1 \le y \le 4$, $6 - y \ge 2$, so every strip of $R$ crosses $x = 2$; the part to the right has strips of length $4 - y$.

2. 02

   $\int_1^{4} (4 - y)\,dy = \left[4y - \frac{y^{2}}{2}\right]_1^{4} = 8 - \frac{7}{2} = \frac{9}{2}$ square units, which is $\frac{21}{2} - 6$.