Comparison Theorem and Limits of integration

[Painguy]

Homework Statement

Why is it that when using the comparison theorem my limits of integration must be from a constant value to infinity and not from negative infinity to infinity?

For example ∫ x/(1+x^2) dx from -∞ to ∞

 

[jbunniii]

Can you be more specific about what comparison theorem you are talking about?

For your example, notice that if $x \geq 1$, you can easily check that
$$\frac{x}{1+x^2} \geq \frac{1}{2x}$$
What does that tell you?