6.1 Areas Between Curves/5

${\begin{aligned}&\color {red}\mathbf {y=x+1} &\color {royalblue}\mathbf {y=9-x^{2}} \\&x=-1&x=2\\\end{aligned}}$

$\int _{-1}^{2}\left|(9-x^{2})-(x+1)\right|dx$

${\begin{aligned}8-x^{2}&=x^{2}\\-2x^{2}&=-8\\x^{2}&=4\\x&=\pm 2\end{aligned}}$