There is a curve representing y=f(x) and the classic problem of finding the area under the curve above the x-axis and between two boundaries, a and b. Without calculus, better approximations can be obtained by dividing the section into smaller sections with equal or unequal widths. The area of each rectangle defined by these sections can be approximated by f(xi)*Δxi, summed up for all rectangles. By making Δx smaller and increasing the number of rectangles (n approaching infinity), a more accurate approximation of the area can be achieved. This leads to considering the limit as n approaches infinity or as Δx becomes infinitesimally small.