6.1 Areas Between Curves/5

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

Failed to parse (syntax error): {\displaystyle \int_{-1}^{2}[(9-x^{2}) - (x+1)] dx &= [9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x]\Bigg|_{-1}^{2} = [9(2)-\frac{(2)^{3}}{3}-\frac{(2)^{2}}{2}-(2)-(9(-1)-\frac{(-1)^{3}}{3}-\frac{(-1)^{2}}{2}-(-1))] &= 18-\frac{8}{3}--2-2+9-\frac{1}{3}+\frac{1}{2}-1 = 19.5 }