What is the difference between(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int_{-\infty}^{\infty} \frac{x}{1+x^2}dx[/itex]

and

[itex]\lim_{R\rightarrow \infty}\int_{-R}^{R} \frac{x}{1+x^2}dx[/itex] ?

And why does the first expression diverge, whilst the second converges and is equal to zero?

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# Convergence of improper integrals

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