# Integrate Box Function?

Calculus Level 3

$\int_1^3 \lfloor x \rfloor \cos \left( \dfrac\pi2 \big( x - \lfloor x \rfloor \big) \right) \, dx$

The integral above is equal to $$\frac a{b\pi}$$, where $$a$$ and $$b$$ are coprime positive integers.

Find $$a+b$$.


Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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