Today, I needed to compute an average value of a function. The problem was that the function was a chart in a .gif image.
I run across a great application called ImageJ. It has a pluggable interface, many powerful functions, it is open-source and written in Java. The platform independent distribution has only 3MB.
I opened my image in the application, cropped the unnecessary parts, and used the magic wand to selected the area under the function line. Then I just clicked on measure and got the area of 69035 pixels (btw. this is the value of the integral). I divided the number by the width of the image and got 226. Now I subtracted 226 from the image height and looked at the y-axis for the average value - 8.7...
Disclaimer: ImageJ is being developed at the National Institutes of Health by an employee of the Federal Government in the course of his official duties. Pursuant to Title 17, Section 105 of the United States Code, this software is not subject to copyright protection and is in the public domain. So long and thanks for ImageJ!