I thought I had the process but I was off apparently. The equations are y=sin^2(pi x/4), y=cos^2(pi x/4) 0, greater or equal to x, greater or equal to 1)
You want four subintervals of the interval interval , so they are each of length , and have mid points , or:
are the interval mid points, where are the limits of integration, and is the number of subintervals.
Then:
or writing
which is the sum of the function at the mid points of the intervals times the interval length
CB