5.4 Indefinite Integrals and the Net Change Theorem/21

${\begin{aligned}\int _{0}^{2}(6x^{2}-4x+5)dx&={\frac {6x^{2+1}}{2+1}}-{\frac {4x^{1+1}}{1+1}}+{5x}{\bigg |}_{0}^{2}={\frac {6x^{3}}{3}}-{\frac {4x^{2}}{2}}+{5x}{\bigg |}_{0}^{2}=2x^{3}-2x^{2}+{5x}{\bigg |}_{0}^{2}\\[2ex]&=[2(2)^{3}-2(2)^{2}+{5(2)}]-[2(0)^{3}-2(0)^{2}+{5(0)}]=16-18+0\\[2ex]&=18\end{aligned}}$