5.3 The Fundamental Theorem of Calculus/19

${\begin{aligned}\int _{-1}^{2}(x^{3}-2x)dx&={\frac {x^{4}}{4}}-{\frac {2x^{2}}{2}}{\Bigg |}_{-1}^{2}\\[2ex]&=\left[{\frac {(2)^{4}}{4}}-{\frac {2(2)^{2}}{2}}\right]-\left[{\frac {(-1)^{4}}{4}}-{\frac {2(-1)^{2}}{2}}\right]\\[2ex]&=[0]-\left[{\frac {1}{4}}-1\right]=0-\left[-{\frac {3}{4}}\right]={\frac {3}{4}}\end{aligned}}$