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First you need to grab the newsid from $_POST after you submit the form. I also changed your SQL code a little. Use these two lines below in place of your SQL line and it will work:
$newsid = $_POST['newsid'];
$result = mysql_query("UPDATE `news` SET `title` = '$title', `text1` = '$text1' WHERE `newsid` = $newsid LIMIT 1",$connect);
Also it seems like you have Global Variables turned on. YOu should call variables with their full name. For example you have <form action="<?php echo $PHP_SELF ?>" method="post">, but you shoudl really have it <form action="<?php echo $_SERVER['PHP_SELF']; ?>" method="post">
dajawu didn't mention this, but he also corrected your use of single quotes to back-ticks. They are different characters. The names of tables and fields of tables may be enclosed in back-ticks ( ` ), but not single quotes ( ' ).