No badge on mail-app until I open app

My problem is: I can't get the mail app to show a badge. I tried what many people suggest, reinstalling the app, but that didn't resolve the issue. Even if I definitely have new emails the app won't show the badge, or any other notification, even though they are all activated for every email. The ONLY way to make the badge appear is AFTER I open the app, THEN its suddenly there. Awesome, but this way its worthless. I wan't to see if there are new mails BEFORE I open the app... Same with the banner, it only appears AFTER I open the mail app. This can't be normal???