Author: Stefano Ghio
Mail: otacorp@gmail.com
Project name: Auto Answer
State: Unsupported
This project is based on the source code from Matt Hahnfeld (http://everysoft.com/) found at http://code.google.com/p/auto-answer/ released under a GNU GPL v3 licence http://www.gnu.org/licenses/gpl.html
Since at the time the app hadn't been released on Google's Play Store yet, I catered his code to my needs last year to add that setting to my LG Optimus HUB which didn't have it (LG thing I was told). It works perfectly, I tested it on Android Gingerbread 2.3.4 and Ice Cream Sandwich 4.0.3 (LG Optimus L7), but should work on Froyo 2.2 too.
The code apparently does not work on Android 5+, but I will not adapt it since at the time there weren't many (read: none) free apps that did this but now you have some choices - https://play.google.com/store/search?q=autoanswer&c=apps and some manufacturers already include this functionality by default.
The licence remains the same: GNU GPL v3.
More info at http://groglogs.blogspot.it/2013/08/android-auto-answer-app.html