5.4 Indefinite Integrals and the Net Change Theorem/29

${\begin{aligned}\int _{-2}^{-1}\left(4y^{3}+{\frac {2}{y^{3}}}\right)dy&=\int _{-2}^{-1}\left(4y^{3}+2y^{-3}\right)dy\\[2ex]&=\left[y^{4}-y^{-2}\right]_{-2}^{-1}\\[2ex]&=(1-1)-\left(16-{\frac {1}{4}}\right)\\[2ex]&=-{\frac {63}{4}}\end{aligned}}$