In the documentation of Date::Calc, there is a recipe for just this question:

How do I check whether a given date lies within a certain range of dates?

use Date::Calc qw( Date_to_Days );

  $lower = Date_to_Days($year1,$month1,$day1);
  $upper = Date_to_Days($year2,$month2,$day2);

  $date = Date_to_Days($year,$month,$day);

  if (($date >= $lower) && ($date <= $upper))
  {
      # ok
  }
  else
  {
      # not ok
  }
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There are other modules like Date::Manip or Class::Date if you want alternatives, but it is sensible to use a module instead of "reinventing the wheel"