$[4]11.$ Express the limit $A$ as a definite integral $($do not evaluate the limit or the integral$)$:

$A=\underset{n}{lim}[{\displaystyle \underset{k=1}{\overset{n}{}}}\frac{\frac{k}{n}}{1+(\frac{k}{n}{)}^4}]\frac{1}{n}$

$=\underset{n}{lim}[\frac{\frac{1}{n}}{1+(\frac{1}{n}{)}^4}+\frac{\frac{2}{n}}{1+(\frac{2}{n}{)}^4}+\frac{\frac{3}{n}}{1+(\frac{3}{n}{)}^4}+...+\frac{\frac{n-1}{n}}{1+(\frac{n-1}{n}{)}^4}+\frac{\frac{n}{n}}{1+(\frac{n}{n}{)}^4}]\frac{1}{n}$