f(x)=2x^3-x^2+1 [1,4]=interval

Using the limit process, (once with right endpts, and the other with left entdpts.) find the area under the curve and above the x-axis on the given interval

i got the area to be 107.5 for right endpts. (not sure if its right) but what about the left endpt??

You are evidently approximating the integral with rectangles . However except for saying you want it done both with left and right endpoints you do not say how many rectangles to use. If you use enough of them you will get the exact answer, which Dr. WLS gave you last night.