Can it be possible?

Calculus Level 3

Does there exist a function f:[1,1]R f: [ -1, 1 ] \rightarrow \mathbb{R} that is not Riemann integrable, but f2 f^2 (defined as f2(x)=(f(x))2f^2(x) = (f(x))^2 for all xx) is Riemann integrable?

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