Let $\displaystyle I(b)=\lim _{ n\rightarrow \infty }{ \int _{ b }^{ \infty }{ \frac { n }{ 1+{ n }^{ 2 }{ x }^{ 2 } } dx } }$, where $b$ is a real number.

Let the sum of all the values $I(x)$ can take be $A$. Find $\lfloor A \rfloor$.

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