  Active solar-type stars show large quasi-periodic brightness variations
caused by stellar rotations with star spots, and the amplitude changes as the
spots emerge and decay. The Kepler data are suitable for investigations on the
emergence and decay processes of star spots, which are important to understand
underlying stellar dynamo and stellar flares. In this study, we measured
temporal evolutions of star spot area with Kepler data by tracing local minima
of the light curves. In this analysis, we extracted temporal evolutions of star
spots showing clear emergence and decay without being disturbed by stellar
differential rotations. We applied this method to 5356 active solar-type stars
observed by Kepler and obtained temporal evolutions of 56 individual star
spots. We calculated lifetimes, emergence and decay rates of the star spots
from the obtained temporal evolutions of spot area. As a result, we found that
lifetimes ($T$) of star spots are ranging from 10 to 350 days when spot areas
($A$) are 0.1-2.3 percent of the solar hemisphere. We also compared them with
sunspot lifetimes, and found that the lifetimes of star spots are much shorter
than those extrapolated from an empirical relation of sunspots ($T\propto A$),
while being consistent with other researches on star spot lifetimes. The
emerging and decay rates of star spots are typically $5 \times 10^{20}$ $\rm
Mx\cdot h^{-1}$ ($8$ $\rm MSH\cdot h^{-1}$) with the area of 0.1-2.3 percent of
the solar hemisphere and are mostly consistent with those expected from
sunspots, which may indicate the same underlying processes.
