5.3 The Fundamental Theorem of Calculus/33

$\int _{1}^{2}\left(1+2y\right)^{2}dy=\int _{1}^{2}\left(4y^{2}+4y+1\right)dy=1y+{\frac {4y^{3}}{3}}+{\frac {4y^{2}}{2}}{\bigg |}_{1}^{2}=2+{\frac {32}{3}}+{\frac {16}{2}}-\left(1+{\frac {4}{3}}+{\frac {4}{2}}\right)={\frac {49}{3}}$