By default
script tags are not parsed and evaluated by browsers when you try to inject them as regular text ( for example using innerHTML). Following code borrowed from mootools library will do it for you.
var myText = "html here <script>alert('javascript eval worked');</script>";
var scripts = [];
var regexp = /<script[^>]*>([\s\S]*?)<\/script>/gi;
while ((script = regexp.exec(myText))) scripts.push(script[1]);
scripts = scripts.join('\n');
if (scripts) (window.execScript) ? window.execScript(scripts) : window.setTimeout(scripts, 0);