# Maximize the integral!

Calculus Level 5

When $$\displaystyle{\int_{0}^{1} f(x) dx =0}$$ and $$-1 \le f(x) \le 1,$$ the maximum value of

$\int_{0}^{1} \left(f(x)\right)^3dx$

is $$X.$$ Find $$[100X] .$$

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