(I appreciate the observation that the midpoint method is more accurate in this case - in fact, it gives the exact result!
Well done drawing that region! It was surprising how many students had trouble drawing the squiggly graph at left.
In this problem I'm sure that it helped this student to draw in the graph of f.
Actually the integral function is well defined at 8 (even though the derivative function isn't defined there!). One point doesn't affect an integral, since it represents area, and there is zero area associated with any individual point. But it was a good observation by the student.
The last line reads "...and therefore the total change will always be positive with respect to that day."