${\int }_0^{21} [x{]}^{4}dx$ is equal 

$\begin{array}{l}{\int }_0^{21} [x{]}^4\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}dx=\sum _{r=0}^{20} {\int }_r^{r+1} [x{]}^{4}dx\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}=\sum _{r=0}^{20} r^4={\left(\frac{20\times 21}{2}\right)}^2=44100\end{array}$