Answer
$a)\int f(x)=7x^{3}+5x^{2}+9x+c$
$b)\frac{d}{dx}\int f(x)=21x^{2}+10x+9$
Work Step by Step
$a) f(x)=21x^{2}+10x+9$
using the rules for general antiderivatives;
$\int f(x)= \int 21x^{2}dx+ \int 10xdx+\int9dx$
$=\frac{21x^{2+1}}{2+1}+\frac{10x^{1+1}}{1+1}+9\int dx+c$
$=\frac{21}{3}x^{3}+\frac{10}{2}x^{2}+9x+c$
$$=7x^{3}+5x^{2}+9x+c$$
$b)$
We know that,
$\frac{d}{dx}\int f(x)= f(x)$
hence, $$\frac{d}{dx}\int f(x)=21x^{2}+10x+9$$
