Draw a rough sketch for the curve y =2+| x +1|. Using integration, find the area of the region bounded by the curve y =2+| x +1|, x =-4, x =3 and y…

Correct Graph: \[\begin{aligned} \text { Required area }= & \int_{-4}^{-1}(2+|\mathrm{x}+1|) \mathrm{dx}+\int_{-1}^{3}(2+|\mathrm{x}+1|) \mathrm{dx} \\ = & \int_{-4}^{-1}(1-\mathrm{x}) d \mathrm{x}+\int_{-1}^{3}(3+\mathrm{x}) d \mathrm{x} \\ & =-\left.\frac{(1-\mathrm{x})^{2}}{2}\right|_{-4} ^{-1}+\left.\frac{(3+\mathrm{x})^{2}}{2}\right|_{-1} ^{3} \\ & =\frac{21}{2}+16=\frac{53}{2} \end{aligned} \]