Understanding Improper Integrals with Limits at Infinity

[sinequanon]

Homework Statement

\int(2dx/(x^2+4)
from x= -\infty to x=2

Homework Equations

No specific ones.

The Attempt at a Solution

So, from there I tried to split the integral into two, integrating between 2 and -2, and -2 and -\infty, but I got very lost trying to take the limits for these, partly because I don't know what to set as the approaching variables in each case. And integrating the function actually is another issue. Could someone take a look?

 

[rock.freak667]

I think you need to integrate that over.

\int \frac{1}{x^2+4} \neq lnG(x)