5.4 Indefinite Integrals and the Net Change Theorem/43

Failed to parse (syntax error): {\displaystyle \int\limits_{-1}^{2}(x-2|x|)dx = \int\limits_{-1}^{0}(x-2(-x))dx + \int\limits_{0}^{2}(x-2(x))dx \\[2ex] }

$=\left({\frac {1}{2}}{x^{2}}+x^{2}\right){\bigg |}_{-1}^{0}+\left({\frac {1}{2}}{x^{2}}-x^{2}\right){\bigg |}_{0}^{2}0-\left({\frac {1}{2}}(-1)^{2}+(-1)^{2}\right)+\left({\frac {1}{2}}(2)^{2}-(2)^{2}\right)-0=\left({\frac {1}{2}}+1\right)+\left({\frac {1}{2}}(4)-4\right)$