Algebra Level pending

Let $$f(x)=max|x^2-4ax|\ \forall\ 0\leq a\leq 1$$ then which of the statements are true?

$$S_{1}:f(1)=1$$

$$S_{2}:f(-1)=5$$

$$S_{3}:\displaystyle\int_{0}^{4} f(x) dx=24$$

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