Consider the limit of summed terms (attachment). Could someone please explain why each of the sums in the 'attached' expression gives an over-estimate of the area beneath y=x^2 +3, between x=0 and x=1.

****I'm rephrasing my question in LATEX so that more posters are attracted to assist me (please).

Could someone please explain why each of the sums in the above expression gives an over-estimate of the area beneath the curve , betweenx=0 andx=1 *****