Optional LIMIT for function grabbing all post with PDO

I'm trying to create a function that will grab all posts within a table. I also wanted to add a optional LIMIT parameter. Here is an example:

function get_all_posts($conn, $limit = 0) {
	if ($limit > 0) {
		$stmt = $conn->prepare("SELECT * FROM posts LIMIT :limit");
		$stmt->execute(array(
			':limit' => $limit
		));
		$results = $stmt->fetchAll();
		return $results ? $results : false ;
	} else {
		$stmt = $conn->prepare("SELECT * FROM posts");
		$stmt->execute();
		$results = $stmt->fetchAll();
		return $results ? $results : false ;
	}
}

PHP:

If I call the function without using the limit parameter it works and displays all the posts. But if I call the function like this: get_all_posts($conn, "1"); Then I get this error:

Fatal error: Uncaught exception 'PDOException' with message 'SQLSTATE[42000]: Syntax error or access violation:
 1064 You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the
 right syntax to use near ''1'' at line 1' in /Applications/MAMP/htdocs/sandbox/blog2/functions.php:19 Stack trace: #0
 /Applications/MAMP/htdocs/sandbox/blog2/functions.php(19): PDOStatement->execute(Array) #1
 /Applications/MAMP/htdocs/sandbox/blog2/index.php(12): get_all_posts(Object(PDO), '1') #2 {main} thrown in 
/Applications/MAMP/htdocs/sandbox/blog2/functions.php on line 19

Code (markup):

Can anyone show me where I've gone wrong?

Thanks!

 

example found by google

$statement = $conn->prepare("SELECT id,username FROM public2 WHERE username = :name LIMIT :limit OFFSET :offset");
$name = "Lei Lei";
$statement->bindValue(':name', $name);
$statement->bindValue(':limit', (int) $start, PDO::PARAM_INT);
$statement->bindValue(':offset', (int) $per_page, PDO::PARAM_INT);
$statement->execute();

Code (markup):