Answer
$$9$$
Work Step by Step
$$\eqalign{
& \int_{ - 1}^2 {\int_y^{4 - y} {dx} dy} \cr
& {\text{Integrate with respect to }}x \cr
& = \int_{ - 1}^2 {\left[ x \right]_y^{4 - y}dy} \cr
& {\text{Evaluating the limits}} \cr
& = \int_{ - 1}^2 {\left( {4 - y - y} \right)dy} \cr
& = \int_{ - 1}^2 {\left( {4 - 2y} \right)dy} \cr
& {\text{Integrate}} \cr
& = \left[ {4y - {y^2}} \right]_{ - 1}^2 \cr
& {\text{Evaluating}} \cr
& = \left[ {4\left( 2 \right) - {{\left( 2 \right)}^2}} \right] - \left[ {4\left( { - 1} \right) - {{\left( { - 1} \right)}^2}} \right] \cr
& = 4 + 5 \cr
& = 9 \cr} $$
