How to properly submit a email within php

Question

I have this script below but i need someone to assist me. It isn't submitting to me it says it is successful because it redirects to the thank you page but i don't receive any email.

What else should i check to make sure that the mail does send? Is my syntax correct? I don't get any errors.

Here is my script

<?


$name = $_POST["name"];
$to = "[email protected]";
$subject = "News Letter Request";


$body = "
<table>
    <tr>
        <td valign='top'>Please Add ".$_POST["email"]." to your mailing list.</td></tr></table>";

$time = date("Y-m-d H:i:s");

$random_hash = md5(date('r', time()));
//define the headers we want passed. Note that they are separated with \r\n
$headers = "From: [email protected]\r\nReply-To: [email protected]";
//add boundary string and mime type specification
$headers .= "\r\nContent-Type: text/html; boundary=\"PHP-alt-".$random_hash."\"";
//define the body of the message.
ob_start();

ini_set ("sendmail_from","[email protected]");


if (mail($to, $subject, $body, $headers)) {
header("Location: http://www.example.com/thankyou.php");
exit(0); 
 } else {
  echo("<p>Message delivery failed...</p>");
 }
echo "Test messages has been sent to ".$to." successfully on ".$time;
?>