Acarpenter is cutting a table leg that is 2 1\4 ft long. what is the greatest possible error?

What is the width of each interval?  To answer this, subtract -1 from 2.  Result:  3.  If n=6, then the width of each interval is 3/6, or 1/2.

If we're to use the left endpoints, then the x values in question are {-1, -1/2, 0, 1/2, 1, 3/2, 2}.

Evaluate the given function at these 6 x-values.  Answer set (to 2 decimal place accuracy):  {3,3.75, 4, 3.75, 3, 1.75).

Now calculate each of the 6 sub-areas under the curve.  To do this, multiply each of the 6 "heights" given immediately above by the subinterval width (1/2).  You will then have 6 subareas.  Find the sum of these 6 subareas.

Your result here is the approx. area under the curve of f(x)=7-x between x=-1 and x=2.