where [tex]t_0=0,t_1=1,t_2=2,t_3=4,t_4=5[/tex], and we define [tex]\Delta t_i=t_i-t_{i-1}[/tex] for [tex]i\ge1[/tex]. The sum is adding up the areas of several trapezoids, each with dimensions determined by the values of [tex]t_i[/tex] and [tex]R(t_i)[/tex]. (See the picture below)