You are right! It does find the area UNDER the curve. However, it is not just any ordinary area. The x-axis (or h-axis) measures distance (that is length). The y-axix measures dt/dh which is the rate of change of time with respect to distance (h). That is the y axis measures time/length. If you have a square with corners (0,0),(a,0),(0,b),(a,b) in the dt/dh versus h plane, it's area is just a*b and the units are length*time/length = time. So the area actually signifies time!