# Golden ratio

Calculus Level 4

$\large \displaystyle\int _{ 0 }^{ 2 }{ \left\lfloor { x }^{ 2 }-x \right\rfloor \, dx } =a-b\phi$

The equation above holds true for positive integers $$a$$ and $$b$$, and $$\phi$$ denotes the Golden ratio, $$\phi = \dfrac{1+\sqrt5}2$$. Find $$a+b$$.

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