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 \(b\), where \(\phi = \frac{1+\sqrt5}2 \) is the golden ratio.

Find \(a+b\).

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