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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