Is there a way in excel that I could get area under a curve ?

To my knowledge, there is not a built in "integration" function. With a knowledge of calculus, one should be able to program the spreadsheet to perform these tasks.

1) Identify the desired integration algorithm. Your reference to "(bar) rectangles" suggests that you are thinking of numerical integration with Riemann sums rather than using the fundamental theorem of calculus. Which Riemann sum (left hand sum, right hand sum, mid point sum, or other) are you interested in (or just pick one and start programming).
2) I would build a table of values like this:

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The chart to illustrate this process should be a relatively simple column+line/scatter chart. I haven't thought it all the way through, but can you readily identify a step in creating such a combination chart that you get stuck on? Sometimes it is easier to focus a response on the specific part that you don't know rather than try to develop the entire thing from scratch.

Hi -

You have to write the integrated equation in Excel and then have Excel graph it.

For example, for the simple case of a line defined at Y=X, the area under that "curve" is the integration of Y=X, which is Y=1/2*X^2.

Then just create a table in Excel where you have Values of X in one columm (e.g., 1, 2, 3, 4, 5, .....) and the resultant Y's in the adjacent column (0.5, 2, 4.5,...). Then have Excel create a bar chart. Go through the same process for more complex equations.

If you have a set of data and you want to create an equation that matches that data, you can use the LINEST function which will best fit a straight line through the data, or use the LOGEST function for exponential shaped data. If your data looks linear, then LINEST would be the best bet and then let Excel help you write the equation of the best fit line, then integrate that equation to determine the area. Same process for non-linear data.

Hope that helps.