Putnam 1993 A1

The horizontal line $y=c$ intersects the curve $y = 2x - 3x^3$ in the first quadrant as in the figure. Find $c$ so that the areas of the two shaded regions are equal. [Figure not included. The first region is bounded by the $y$-axis, the line $y=c$ and the curve; the other lies under the curve and above the line $y=c$ between their two points of intersection.]