I just found this App (Battery Repair) on the Google Play Store, my question is how can it make my battery last longer. What optimazions are they doing? Has anyone tested this tool, does it work?
No app can "optimize" or "maintain" the battery in any way as it can't get the necessary access to the hardware -- probably not even if it required root. This app explicitly advertises that it does not. Anyway, the manufacturer's engineers surely have already implemented all the necessary optimizations. There is no way that the app's developers knows anything useful about every phone's charging circuitry and battery that the engineers don't.
In short, there is no way this app does anything useful at all. (It might even be malware, but I don't get that impression in this case).
(Note: the following is probably not true)
The only thing an app can do (on a rooted phone) is to recalibrate the battery. If the battery is miscalibrated the OS might think that it is as good as empty and force a shutdown although there is still a useful amount of charge left. One app that does this is the aptly named Battery Calibration.
I installed this app yesterday with some uncertainty and it detected (and fixed) a number of problems. I then found this thread which made my suspicions even more so. Today I ran the app and it detected zero problems, not surprising since the battery presumably got no new problems overnight. Out of curiosity I set the date to a month in advance and ran the test again, and suddenly there are eight 'cells' with low charge and two inactive! So obviously all this app does is check when it was last run and the longer ago it was the more 'faulty' cells it throws up in a random pattern to make it look like it's found 'faults' which it can then fix.
Don't waste your time, I assume the only thing this does is provide ad revenue to the developer.