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}}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int_{-1}^{2}[(9-x^{2}) - (x+1)] dx &= [(9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x)]\Bigg|_{-1}^{2} \\[2ex] &= \left[9(2)-\frac{(2)^{3}}{3}-\frac{(2)^{2}}{2}-(2)\right]-\left[(9(-1)-\frac{(-1)^{3}}{3}-\frac{(-1)^{2}}{2}-(-1))\right]] \\[2ex] &=[18-\frac{8}{3}-2-2]-[-9+\frac{1}{3}-\frac{1}{2}+1] \\[2ex] &= \frac{117}{6} \\[2ex] \end{align} }