I couldn't get LaTEX to display this one, it kept erroring out after about 3/4 of the equation was entered. So I pasted a jpg instead. Thanks for looking.
Sorry forgive me. I saw something else in the problem and made a mistake.
The function is,
Then, the convergent riemann sum is, (by definition)
Has property that,
Then by the Fundamental Theorem of Calculus (eventhough I am angry when it is referred to as like this. It certainly is not a fundamental theorem at all!)
You must first write the sum in a general way as I did for you. You are setting up rectangles partitioned ...etc and letting n approach infinity for the rectangles height, and the width of each rectangle is . Now when you apply the limit, the infinite sum tranforms into the integral .