use feature qw( say );;
use DateTime;

my $dt = DateTime->new(
   year      => 2003,
   month     => 4,
   day       => 5,
   hour      => 2,
   time_zone => 'America/Chicago',
);
$dt->set_time_zone('UTC');
$dt->add( days => 1 );                                                
$dt->set_time_zone('America/Chicago');
say $dt;    # ERROR: 2003-04-06T03:00:00