#$10{\displaystyle \underset{0}{\overset{2}{}}}(4x+x^3)dx$ using the

definition $of$ the definite integral $asa$

$limitof$ Riemann sums. You may wish

$to$ use these summation formulas:

${\displaystyle \underset{i=1}{\overset{n}{}}}i=\frac{n(n+1)}{2},{\displaystyle \underset{i=1}{\overset{n}{}}}{i}^3=(\frac{n(n+1)}{2}{)}^3$

$Be$ sure $to$ use proper notation andwords

$to$ explain your a solution" $In$ particular,

use words "sample points" and "Riemannsam",