My phone had an old battery that kept lying about its battery life to me; it would start at %100, shut down, say it had low battery, force me to keep pressing the power button unitl it would turn on and say it had 10%, shut down again, show the low battery icon again, then force me to turn it on to show the real battery percentage, which was way lower than it should have been.
I have to say it was not as easy as I anticipated. The first difficult part was removing the adhesive from underneath the battery. It did not pull out in one go like it showed in the instructions, I had to keep ripping it bit-by-bit until it was fully underneath the battery and I had no way of getting to it. My last resort was to PEEL the battery back with the skinny black tool and pick out more of the adhesive with my tweezers. I know the battery clearly said not to bend or puncture it, but it was the only way of getting it out at that point, and it wasn't like I was going to be using it in the future anyway. It did take some time but nonetheless I did manage to extract the battery with the rest of my phone intact.
Another problem I had was trying to reconnect the digitizer cable back to its socket. It didn't have any pieces on the sides that I could press into like the other cables, but the instructions clearly stated I coudn't press down in the center of the plug, so I had trouble keeping it properly installed. After countless tries of screwing, closing, opening again, and unscrewing the phone apart to make the touchscreen function properly, I was finally able to CAREFULLY connect the digitizer cable into its rightful place.
Now my phone's battery runs like new and I rarely have to charge it!
Make sure you have the patience and time for this kind of thing, and read the instructions carefully BEFORE the procedure like you would in any lab experiment.