Partition this integral!

Calculus Level 3

\[\large \int_{1}^{\infty} \dfrac {2x\{x\} - \{x\}^2} {x^2 \lfloor x \rfloor ^2} \, dx \]

If the integral above can be expressed as \( \dfrac{\pi^a - b} c \), where \(a,b,c\) are all positive integers, find \(a+b+c\).

Notations:

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