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).

$\displaystyle \lim_{n \to 0} \frac {1}{n} \Sigma^{\infinity}_{k=1}\(\frac{k^2}{n^2} + 3)$

Could someone please explain why each of the sums in the above expression gives an over-estimate of the area beneath the curve $\displaystyle y = x^2 +3$ , betweenx=0 andx=1 *****