${}_{R}f(x,y)dA={\displaystyle \underset{c}{\overset{d}{}}}[{\displaystyle \underset{a}{\overset{b}{}}}f(x,y)dx]dy$

We are given the function $f(x,y)=x+6y.$ Therefore, the integral we are interested in$,$ over the rectangular region $1x2$ and $0y1$ is as follows.

${\displaystyle \underset{0}{\overset{1}{}}}[{\displaystyle \underset{1}{\overset{2}{}}}()dx]dy$