Integrate on Floors

Calculus Level 4

11x+x+xdx= ? \large \displaystyle \int _{ -1 }^{ 1 }{ \left\lfloor x+\left\lfloor x+\left\lfloor x \right\rfloor \right\rfloor \right\rfloor \, dx } = \ ?

Give your answer to 3 decimal places.

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