Given series ${\displaystyle \underset{1}{\overset{}{}}}\frac{1}{n^3+n}$

a$)$ Find the corresponding function $f(x).$

b$)$ Show that $f(x)$ satisfies the $2$ conditions of the integral test on interval $[1,).$

c$)$ Evaluate ${\displaystyle \underset{1}{\overset{}{}}}f(x)dx$

d$)$ Use the result of part c$)$ to determine whether the series is convergent or divergent.

Please show step by step. Minimum written explaination Thanks.