If you are familiar with jQuery syntax, PHP Simple HTML DOM might be good place to start http://simplehtmldom.sourceforge.net/
include('simple_html_dom.php');
$html = file_get_html('http://www.domain.co.uk/page.php');
$result = $html->find('#sidebar-bgbtm', 0)->outertext;
And then export to json:
echo json_encode( array( 'outertext' => $result) );