Automated SUM of a function over a data range?; Requesting Help

Attached is a file that I'm using for a research project. The Interactive Regr Tab shows data over a period of time. I'm using a slider to automatically analyze portions of every profile of electrical current. For example: I can select a range of data with the slider and find characteristics like 'Slope', 'Area' under the curve, etc.

I need help trying to automate the calculation of 'First Moment' in Cell D8. It is a fairly straightforward calculation that I have manually created data for in cells G71:G1384 of the 'Data' tab. The answer for the calculation is a SUM in cell H1384. However, I want to be able to select my data range with my slider and calculate it with a function - not manually calculate this on the 'Data' tab. To do this, it seems like I need to SUM the solution of function over the selected data range. I don't know if this is even possible. Can any of you Excel experts give me a hand with this?

NOTE: To help you decipher the calculation for First Moment about the y-axis, it is the sum of (x*the area of a sliver under the curve) for the entire curve, f(x). X is the distance from the y-axis. The number .01666 in my equation brings the x-value to the center of the 'sliver' of area. Excel_Data_Experiment.xls