6.1 Areas Between Curves/5

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&\color {red}\mathbf {y=x+1} &\color {royalblue}\mathbf {y=9-x^{2}} \\&x=-1&x=2\\\end{aligned}}}

${\begin{aligned}\int _{-1}^{2}[(9-x^{2})-(x+1)]dx&=[(9x-{\frac {x^{3}}{3}}-{\frac {x^{2}}{2}}-x)]{\Bigg |}_{-1}^{2}\\[2ex]&=[9(2)-{\frac {(2)^{3}}{3}}-{\frac {(2)^{2}}{2}}-(2)]-[(9(-1)-{\frac {(-1)^{3}}{3}}-{\frac {(-1)^{2}}{2}}-(-1))]\\[2ex]&=[18-{\frac {8}{3}}-2-2]-[9-{\frac {1}{3}}+{\frac {1}{2}}-1]\\[2ex]&=19.5\\[2ex]\end{aligned}}$