Maximize the integral!

Calculus Level 5

When 01f(x)dx=0\displaystyle{\int_{0}^{1} f(x) dx =0} and 1f(x)1, -1 \le f(x) \le 1, the maximum value of

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

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

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