  Over the past decade, $\gamma$-ray observations of supernova remnants (SNRs)
and accurate cosmic-ray (CR) spectral measurements have significantly advanced
our understanding of particle acceleration in SNRs. In combination with
multiwavelength observations of a large sample of SNRs, it has been proposed
that the highest energy particles are mostly accelerated in young remnants, and
the maximum energy that middle-age and old SNRs can accelerate particles to
decreases rapidly with the decrease in shock speed. If SNRs dominate the CR
flux observed at Earth, a large number of particles need to be accelerated in
old SNRs for the soft CR spectrum even though they cannot produce very
high-energy CRs. With radio, X-ray, and $\gamma$-ray observations of seven
middle-age shell-type SNRs, we derive the distribution of high-energy electrons
trapped in these remnants via a simple one-zone leptonic emission model and
find that their spectral evolution is consistent with such a scenario. In
particular, we find that particle acceleration by shocks in middle-age SNRs
with an age of $t$ can be described by a unified model with the maximum energy
decreasing as $t^{-3.1}$ and the number of GeV electrons increasing as
$t^{2.5}$ in the absence of escape from SNRs.
