Why apps keep opened even when turning the iPhone 5 off then on?

Hi guys, please tell me if this is the current bahviour of iPhone, when turning the device off, with many apps opened in the background, turning it on again, it keeps opened! It's like hibernating your computer, isn't it?
Thank you

They don't.
What makes you think the apps are still open after restarting the phone?
If you are looking at the app icons at the bottom of the screen when you double-tap the home button, then those are NOT running apps. That is simply a list of recently used apps. Which apps you have recently used does not change when restarting the phone.
Most apps on the iPhone do not run in the background anyway.
Read: http://speirs.org/blog/2012/1/2/misconceptions-about-ios-multitasking.html

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