Area Four Ways

We estimate the area under the curve y = 1 + x^2 from -1 to 2 in four ways, all breaking the interval [-1,2] into N=3 pieces. The methods are: 1) Using right endpoints 2) using left endpoints 3) using the trapezoidal rule and 4) using midpoints. Of course N=3 is way too small to get accurate results, but we see how the different methods work.