I found an old .xls file from my backup drive which dates back to year 2004, 4 years before MATHalino.com was being online and 6 years before I start to blog. The file is about the length of arc of the function y = f(x) from x = a to x = b, and the area bounded by y = f(x) and the x-axis from x = a to x = b. The method used to find the length of arc and the area was integration. You may download the file and experiment with it, mess it up, download it again, revise it, claim it as your own, do anything to it, it's up to you. The link is provided below.
 

Download Link:
Length of arc and area by Integration using MS Excel
 

Screenshot:

Example of Integration using MS Excel
The overall idea of this integration is iteration, meaning, we are going to assign a value of x starting from the lower limit and increment x by small amount up to the upper limit. With each x in the iteration, we then find the value of the function and finally sum up all the values to arrive with the answer. As an example, let us integrate the square root of (9 - x) dx with limits from 0 to 9.
 

Microsoft Excel has no direct function for integration, if there is, please inform me through the comment form below. Now, to carry the integration, let us solve for y at each value of x starting from 0 up to 9, iterating the process 1000 times.
 

We are going to translate this formulas into MS Excel
UL = upper limit = 9
LL = lower limit = 0
dx = (UL - LL) / 1000 = (9 - 0) / 1000 = 0.009
y = sqrt(9 - x)
Answer = sum of y·dx

1. At x = 0, y = 3, y·dx = 0.027
2. At x = 0.009, y = 2.998499625, y·dx = 0.026986497
3. At x = 0.018, y = 2.996998498, y·dx = 0.026972986
4. And so on, incrementing x by 0.009 in each iteration until we reach the upper limit 9.
5. To find the answer of integration, simply sum up all the values of y·dx.

Download the example file below to see how we implement this work and look at the formula bar at each cell. If you have specific question about the formula in the Excel file, please use the comment from below so that I can answer it for you.
 

Download example file: MS Excel Integration Example