My code for creating an admin option doesn’t work

Make Sure Your Functions, Slug and Callback Functions are Unique(Means Different from any other plugin or default WordPress). Also to save options use Settings API
http://codex.wordpress.org/Function_Reference/register_setting

<?php
add_action('admin_menu', 'add_unique_custom_options');
function add_unique_custom_options()
{
    add_options_page('Global Custom Options', 'Global Custom Options', 'manage_options', 'unique-functions','unique_custom_options');
}
function unique_custom_options()
{
?>
    <div class="wrap">
        <h2>Global Custom Options</h2>
        <form method="post" action="options.php">
            <?php wp_nonce_field('update-options') ?>
            <p><strong>Twitter ID:</strong><br />
                <input type="text" name="twitterid" size="45" value="<?php echo get_option('twitterid'); ?>" />
            </p>
            <p><input type="submit" name="Submit" value="Store Options" /></p>
            <input type="hidden" name="action" value="update" />
            <input type="hidden" name="page_options" value="twitterid" />
        </form>
    </div>
<?php
}