# 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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