Question: what is the difference between a left hand sum and a right hand sum?
Answer: Any left-hand sum will be an under-estimate of the area of R. Since f is increasing, a left-hand sum will use the smallest value of f on each sub-interval. ... Any right-hand sum will be an over-estimate of the area of R. Since f is increasing, a right-hand sum will use the largest value of f on each sub-interval.