Let S denote the locus of the mid-points of those chords of the parabola y² = x, such that the area of the region enclosed between the parabola and the chord is 4/3. Let ℛ denote the region lying in the first quadrant, enclosed by the parabola y² = x, the curve S, and the lines x = 1 and x = 4. Then which of the following statements is (are) TRUE?