Irregular Data Interval Numerical Integration

I have this dataset with ~21,000 points. I need to integrate at ~44,000 regular intervals, but the data is spaced irregularly. Here's an image of a small subset for context:
Data.png

The vertical grey lines are the intervals I need to integrate at (1 unit). The circles represent the data points. I'm trying to come up with some sort of algorithm that will allow me generate a new data set. I'm not sure if this is more an Excel programmer question or a math question, so I'm posting this to a math forum as well.

I've attached a CSV of the points in the above image in case you want to experiment. Any ideas?

"What is your desired integration algorithm? Trapezoid rule?"
I was getting wrapped up in Simpsons rule, but your comments make feel like I was going astray. Also, another point of fact, the domains of dataset I'm looking for is equal to the domain of the original set.


"Expanding the data from 21000 point to 44000 points means that you must add new points to the data set. How do you intend to add those points? Note that simple linear interpolation should yield the same answer as trapezoid integration using the existing 21000 data points, so it seems like superfluous step to turn 21000 points into 44000 points if you intend to use linear interpolation to create the extra points"
I am open to suggestions as to methods, so long as the answer is close to target. I already know the integral of the whole dataset--we can use that as a check. Just to clarify, I need the integral of the curve in one unit intervals. Would you care to show me an example of how you would interpolate the attached dataset?


I'm fairly proficient in Excel, but I'm a master with AutoCAD. I'm devising a way where I might normalize the data there, and reimport to excel, where all my intervals will then align with my data. Not there yet though, so please jump in if you can.

Memory is likely serving you better than I. I can't tell you why I thought Simpson's rule, just that I did. I need the integral of the data I have at single unit domains. I have another dataset that I need to contrast with this one, and it is already configured such that every unit of data is in tabulated form. I am trying to match that. If I can integrate the data as individual integer domains, each integration corresponding to a single data entry in a list of coordinates, then I will end up with the areas bounded by units on the left and right( e.g 5 and 6), zero on the bottom, and the range of the data on the top, totaling 35,040 separate integrations (not 44k, I was mistaken previously). This corresponds to one year at 15 minute intervals. The sample I attached was for one day.

I wanted to follow up and close out this issue. As I said previously, I'm a master with AutoCAD, so I was able to pick new points at the intervals I needed. Took about an hour, and the best thing is it's immediately visually verifiable, whereas the numerical solutions always left me with a sense of doubt, as I can't "see" the numbers. Thank you for your input concerning this matter.