BTW, to be a bit more complex, is there any way I can get the text before each integer using $'?

Here's an attempt at the last part of your question..

This solution uses split. By putting brackets around the regex, we can get it to return pairs of values - the integers and preceeding text.

#!/usr/bin/perl
use warnings; use strict;

use List::Util;

sub get_text_and_ints {

  my @pairs = split(/([+-]?\d+)/);
  my @text = ();
  my @integers = ();

  while (@pairs) {
    push (@text, shift (@pairs));
    push (@integers, shift (@pairs))
      if (@pairs);
  }

  return (\@text, \@integers);
}
#
# Testing
#
foreach (<DATA>) {

  chomp;

  my ($text,$ints) = get_text_and_ints($_);

  my $max_int = List::Util::max (@$ints);

  print "/$_/ - has ".(defined $max_int? "maximum of $max_int":"no int
+egers")."\n";

  for (my $i = 0; $i < @$ints; $i++) {
    print " - integer $ints->[$i] is proceeded by /$text->[$i]/\n";
  }

}
__DATA__
ASBSDEC 34 GADVVEEVEETTE 56 IOEOREAK GKJEOG EFEAF 1090 DAFFEE 3762
ASB C 134 PPKOREAK EFEAF 290
What Is The Sqrt Of -1?
This Line Is Only Text
101 Dalmations
42
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