SAT1000 - P156

Let $f_1(x)=x^2, f_2(x)=2(x-x^2), f_3(x)=\dfrac{1}{3}|\sin 2\pi x|$ .

If $I_k=\displaystyle \sum_{i=1}^{99} |f_k(\dfrac{i}{99})-f_k(\dfrac{i-1}{99})|$ , compare $I_1, I_2, I_3$ .

$A.\ I_1<I_2<I_3$

$B.\ I_2<I_1<I_3$

$C.\ I_1<I_3<I_2$

$D.\ I_3<I_2<I_1$

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Have a look at my problem set: SAT 1000 problems