Counting the volume of block. I am given function $f(x)=\frac{1}{\sqrt{(x^2+1)}}, x\in\mathbb{R}$
I am obliged to find the volume of block which is designated by rotation of $f(x)$. The rotation is made realtive to the axis $OX$. 
I know the eqaution for counting this $V=\pi\int_{a}^{b}{(f(x))^2dx}$
The domain of this function is $\mathbb{R}$. How to determine what $a$,$b$ should i use? Should I do $a=-\infty, b=\infty$? and the count $V=\pi\int_{-\infty}^{\infty}{\frac{1}{x^2+1}dx}$ ?

You are correct. You want $$V=\pi\int_{-\infty}^\infty\frac1{x^2+1}\,dx.$$
