The region bounded below by the parabola y = x² and above by the line y = 4 is to be partitioned into two subsections of equal area by cutting across it with the horizontal line y = c.

a. Sketch the region and draw a line y = c across it that looks about right. In terms of c, what are the coordinates of the points where the line and parabola intersect? Add them to your figure.

b. Find c by integrating with respect to y.

c. Find c by integrating with respect to x.