Personally, I tend to see Time::Local as "the hard way" (due in part to the 0-based/1-based issue) and prefer DateTime::Format::Strptime:

#!/usr/bin/perl

use strict;
use warnings;

use DateTime::Format::Strptime;

my $date_parser = DateTime::Format::Strptime->new(pattern => '%D');

while (<DATA>) {
  print $date_parser->parse_datetime($_)->epoch, "\n";
} 

__DATA__
06/06/2009
01/30/2009
[download]

This example prints the epoch values for each date, as the OP said he wanted to convert them to an integer (and epoch is what the time function returns), but the DateTime suite also includes tools for displaying the date in pretty much whatever format you may want if epoch isn't what you're looking for.