There is no such app for iOS because of its security limitations, you can see such statistics only once jailbroken.
That being said, you will find something close to what you are looking for but only if you are using iOS 9. Do the following: Settings > Battery and under Battery if you scroll down by a little bit, you will see battery usage for the last 24 hours or for the last 7 days in % and in min/h on screen time and background usage also in min/h, something like the image below.
