I think that this exact case is handled in the Camel Book.

The logic is quite straightforward:

#!perl

use strict;
use warnings;

while (<DATA>) {
   chomp; # get rid of pesky newlines
   if(is_integer_string($_)){
       print "$_ is a valid integer string\n";
   }
   else {
       print "$_ isn't a valid integer string\n";
   }
 }
sub is_integer_string {

   # a valid integer is any amount of white space, followed
   # by an optional sign, followed by at least one digit,
   # followed by any amount of white space

   return $_[0] =~ /^\s*[\+\-]?\d+\s*$/;
}
__DATA__
1
1234
 +1234
 -1234
 A
 1234+
+ 1234
[download]

Note that this does not check to see if the integer can be represented on your system. It also does not permit white space between the sign and the leading digit of the number being examined.

return $_[0] =~ /^\s*[\+\-]?\d+\s*$/;
[download]

 if(( $_[0] =~ /^\s*[\+\-]?\d+\s*$/) and ($_[0] > 0)) {
    return 1;
  }
  else{
    return undef;
  }
[download]

Doubtless, this is not the most efficient method.