  We demonstrate that the constraints on the evolution of dark energy
implemented by the DESI collaboration may be insufficient or incomplete using
their own BAO data. Using large enough prior ranges for the present-day
equation of state of dark energy $\omega_0$ and amplitude of dark energy
evolution $\omega_a$, we obtain the complete $1\,\sigma$ and $2\,\sigma$
constraints $\omega_0=1.04^{+0.91+2.00}_{-1.00-1.90}$ and
$\omega_a=-7.4^{+3.8+6.8}_{-3.2-7.3}$ indicating a beyond $2\,\sigma$
preference of quintessence-like dark energy today and an evidence of evolving
dark energy at beyond $2\,\sigma$ CL, respectively. Our results are different
from $\omega_0=-0.55^{+0.39}_{-0.21}$ and the $2\,\sigma$ upper limit
$\omega_a<-1.32$ reported by the DESI collaboration \cite{DESI:2024mwx}.
Employing a data combination of cosmic microwave background, DESI BAO and type
Ia supernova, we obtain the $1\,\sigma$, $2\,\sigma$ and $3\,\sigma$
constraints $\omega_0=-0.707^{+0.089+0.18+0.24}_{-0.089-0.17-0.22}$ and
$\omega_a=-1.09^{+0.38+0.67+0.82}_{-0.31-0.72-1.00}$, which reveals a
$\sim4\,\sigma$ evidence of dynamical dark energy when the redshift
$z\lesssim0.1$. We verify that the BAO data point from luminous red galaxies at
the effective redshift $z_{\rm eff}=0.51$ hardly affects the joint constraint
from the data combination of cosmic microwave background, DESI BAO and type Ia
supernova. We also point out the shortcomings and advantages of the binning
method widely used in cosmological analyses.
