Answer
$a)\int f(x)=-6x^{-1}+7x+c$
$b)\frac{d}{dx} \int f(x)dx=6x^{-2}+7$
Work Step by Step
$a) f(x)=6x^{-2}+7$
Using rules of general antiderivative
$\int f(x)=\int 6x^{-2} dx+\int 7dx +c$....(splitting the terms)
$=\frac{6x^{-2+1}}{-2+1} +7x+c$
$=-6x^{-1}+7x+c$
$b)$ We know that,
$\frac{d}{dx} \int f(x)dx=f(x)$
thus,
$\frac{d}{dx} \int f(x)dx=6x^{-2}+7$
