I know exactly how you feel @Colossus. I was in that position only a few weeks ago.
PHPUnit and unit testing in general is great for when you want to test a small part of your application like a method. A week ago I designed a form whereby a user can add tags to a job they're posting. Those tags are separated by comma's and I wanted to convert the input into an array to insert into a table. I wrote my method within PHPUnit first to assert that the input would be filtered, sanitised and returned as an array. Then I could begin refactoring and extracting the code into a trait. You could have quite easily done this with PHP Spec as well - that is another tool for Unit testing.
My personal favourite though is Codeception. You can use it for Integrated, Acceptance and Unit tests. It hooks into PHPUnit (meaning all PHPUnit methods are available to it) and I find the syntax and simplicity of it all really easy and I can run all of my different types of test all at once.
Regarding your example:
"...for example lets say I have a form with a file upload functionality, and all it has a simple move to specific folder and store the name inside of the database."
Well for that, you could always use PHPUnit or PHPSpec with Mockery to determine that when the file upload class is mocked and a method is called, the result is as you expected (i.e. true, signifying the file was uploaded). And for a more integrated test, you could use Codeception with its Filesystem module to check that an actual file is created ($I->seeFileFound or $I->seeInThisFile).
Jeff had a very good tutorial on Mocking with PHPUnit on tuts+ some time ago and it's quite related to file uploads:
http://code.tutsplus.com/tutorials/easier-testing-with-mockery--pre-69600