Add Laravel 5.1 to my website?

[ebookx10]

I want to test using Laravel, but it does not work correctly.
My goal is to add a subdomain laravel to [mysite].x10.mx
I upload laravel directory (from a fresh install) to my server, and it looks like this:

Then, I create a subdomain from CPanel:

I create 2 route from my laravel app:

// app/Http/routes.php
Route::get('/', function () {
    return "Home Page";
});

Route::get('test', function () {
    return "Test Page";
});

And this is a result (Case 1):

So, the route laravel.[mysite].x10.mx/test does not work here

I make a small change:
- Move and rename HOME/laravel/public to HOME/public_html/public_laravel
- Change some reference in public_laravel/index.php:

require __DIR__.'/../../laravel/bootstrap/autoload.php';
$app = require_once __DIR__.'/../../laravel/bootstrap/app.php';

- Change document root for the subdomain to HOME/public_html/public_laravel
- New site structure:

Finally, it works (Case 2):

I can make it work, but I still don't know why in Case 1, the second route to "/test" lead into error
First, I think that the document root folder of subdomain must be inside the main document root (HOME/public_html), but the first route to "/" in Case 1 still works, so this is not the cause of the error

So, what is the different between inside and outside HOME/public_html that make Case 1 differ from Case 2? Is mod_rewrite module doesn't apply to outside this folder?
Can I make Case 1 work like Case 2?

(Sorry for my poor English)