On the left is a sketch of the graph of the equation y = x², for x between 0 and t.  Take the area in red and revolve it about the y-axis and compare the volume of the resulting solid with the volume similarly generated by the area in blue. You'll discover, as did Jacob Hopping, a student in one of our Calculus II classes, that the two solids have the same volume! (Try it out for yourself.)  Find all other (continuous) functions that have this same property.  (Partial credit for finding all polynomials with the property.)