  The habitability of planets is closely connected with the stellar activity,
mainly the frequency of flares and the distribution of flare energy. Kepler and
TESS find many flaring stars are detected via precise time-domain photometric
data, and the frequency and energy distribution of stellar flares on different
types of stars are studied statistically. However, the completeness and
observational bias of detected flare events from different missions (e.g.
Kepler and TESS) vary a lot. We use a unified data processing and detection
method for flares events based on the light curve from Kepler and TESS. Then we
perform injection and recovery tests in the original light curve of each star
for each flare event to correct the completeness and energy of flares. Three
samples of flaring stars are selected from Kepler and TESS, with rotating
periods from 1 to $\sim$ 5 days. Adopting a hot-blackbody assumption, our
results show that the cumulative flare frequency distributions (FFDs) of the
same stars in Kepler and TESS bands tend to be consistent after correction,
revealing a more natural flaring frequency and energy distribution. Our results
also extend the low-energy limit in cumulative FFD fitting to $10^{31.5-33}$
erg on different types of stars. For solar-type stars, the average power-law
index of cumulative FFD ($\alpha_{\rm cum}$) is $-0.84$, which indicates that
low-energy flares contribute less to the total flare energy. With a piecewise
correlation between $\alpha_{\rm cum}$ and $T_{\rm eff}$, $\alpha_{\rm cum}$
first rises with $T_{\rm eff}$ from M2 to K1 stars, then slightly decreases for
stars hotter than K1.
