find a Riemann Sum formula for evaluation points that are one-third of the way from the left endpoint to the right endpoint.

if the interval is [a,b] and there are n equal subintervals, then the ith x value is a + i times the subinterval width, less 2/3 of that width.

xi = a + (b-a)/n * i - (b-a)/n * 2/3
= a + (b-a)/n * (i - 2/3)

and the sum is as usual

n
∑ f(xi)*(b-a)/n
i=1