Problem:

Prove that the area of the region bounded by the graph of a parabola with equation $y=a\text{}{x}^2$ , $$ a∈ℝ and a horizontal line (region shaded in yellow) is exactly $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ of the area of the corresponding circumscribed rectangle (region shaded with slanting lines). The two upper vertices of the circumscribed rectangle are the intersection points of the parabola and the horizontal line and its lower vertices are on the x-axis. 

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Area Relationship - Parabola & Rectangle