Area under the curves, can you make a right choice?

Calculus Level 2

Take a point AA on the graph of y=f(x),y=f(x), and let BB be a point on the graph of y=xy=\sqrt{x} such that ABAB is parallel to the yy-axis. Call the area bounded by these two curves and the segment ABAB as R.R.

Now, let CC be a point on the yy-axis such that ACAC is parallel to the xx-axis. Call the area bounded by the curve y=f(x),y=f(x), the yy-axis, and the segment ACAC as S.S.

Given that the function ff is continuous and the areas RR and SS are equal, which of the following statements is true?

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