I’m assuming that you want to do something with that html code somewhere?
I have yet to find a way to prevent that function from escaping the quotes, but you could try using the php built-in-function ‘stripslashes()’ to display the html properly anyway, like so:
<?php
$display = '<span style=\"font-weight: bold;\">Bold</span>';//the content
echo stripslashes($display);
?>
This will display your content as if the update_option function hadn’t escaped all the quotes.
