is_int($var) returns true if $var is an integer, not a string containing an integer.
You have $var coming from a form, so it is definitely a string, not an integer.
Try this ...
if(is_numeric($var){
$var += 0; // This converts a numeric string to a number
if(is_int($var){
echo "Integer!";
} else {
echo "Not an integer!";
}
} else {
echo "Not an integer!";
}