SCalcCC$55\mathrm{.}1\mathrm{.}029$

$(a)$ Use the definition given below with right endpoints $to$ express the area under the curve $y=x^3$ from $0to1as$ a $limit.$

$(b)$ Use the following formula for the sum $of$ cubes $of$ the first $n$ integers $to$ evaluate the $limitin$ part $(a).$

$1^3+2^3+3^3+$cdots$+n^3=[\frac{n(n+1)}{2}{]}^2$