Three results for finding the area under the curve y=2xx2+1, between x=0 and x=6, are shown below.

• The result found by dividing the interval into 6 subintervals and then adding up the areas of the inscribed rectangles is approximately 114.72.
• The result found by dividing the interval into 12 subintervals and then adding up the areas of the inscribed rectangles is approximately 131.59.
• The exact result found by evaluating the antiderivative at the bounds is approximately 149.37.

In essay format, explain the differences between these results.