Question

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

Answer 1

so divide the limits by n evenly spaced increments, then each f(x) will be evaluated at each 1/3*increment + xleft.

I am not certain what I can do for you more than this.

Answer 2

So, with limits a and b, that will be

n-1
∑ f(a+(i + 1/3)*(b-a)/n)*(b-a)/n
i=0