Think of a battery as a timer, as the clock ticks down the effectiveness of holding a charge goes down and the battery dies quicker. But replacing that battery will reset the clock so yes it will improve battery life
However you have a little problem with your battery, wether it is a internal battery reading problem or the computer computing the data the battery is sending it
Considering you computer is 6 years old I would recommend replacing the battery and see if that fixes the problem, but if it doesnt just let us know