Nice Function

Calculus Level 5

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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