$\displaystyle f(x)=\frac{2x^2+4x+2}{x^2+1}$

$\displaystyle \lim_{x\ \rightarrow\ \infty}f(x)=$

(I am not familiar with this notation at all... )

$\displaystyle f'(x)=$

$\displaystyle f'(x)=0$ when $\displaystyle x=A,\:B$

$\displaystyle A=\:\:,\:B=$

$\displaystyle \int_A^Bf(x)dx=$

Please help

I'm not even sure where to start. I mean, I can factorise the equation, but would that help? I know that the derivative of the equation is the slope at any given value of $\displaystyle x$, and the slope is 0 for each minima/maxima. But I don't know how to answer these questions...