Partition this integral!

Calculus Level 2

12x{x}{x}2x2x2dx\large \int_{1}^{\infty} \dfrac {2x\{x\} - \{x\}^2} {x^2 \lfloor x \rfloor ^2} \, dx

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

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