5.3 The Fundamental Theorem of Calculus/33

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