Golden ratio

Calculus Level 4

02x2xdx=abϕ \large \displaystyle\int _{ 0 }^{ 2 }{ \left\lfloor { x }^{ 2 }-x \right\rfloor \, dx } =a-b\phi

The equation above holds true for positive integers aa and bb, where ϕ=1+52\phi = \frac{1+\sqrt5}2 is the golden ratio.

Find a+ba+b.

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