Personally, knowing nothing about your story, I'd vote for integrating them in bits and pieces throughout the story, instead of frontloading it as a prologue.
Prologues, if not done well, have a way of slowing things down and feeling a bit lecture-like - as if you're just sititng your audience down and going "okay, here's what you need to know before we can begin the real story" - and they're not always needed. We don't always need to know about the character's childhood for the story to function, and prologues can make your readers feel like they have to wade through a lot of pages before they get to the actual story.
Speaking of specifically how to integrate a backstory in the main plot, I'd say that having a look at how the tv-show Person of Interest does it is useful. At least in the first two seasons, nearly every episode reveals something more about the main characters' backstories in bits and pieces, using flashbacks where it is relevant. Something in the present timeline triggers a memory - or is thematically similar - to something in the backstory of one or more of the characters, and you get a brief scene of the past, before they cut back to the present. Often, the backstory scenes link together to form a small story-arc themselves, telling a small, but complete unit of backstory throughout the episode. Say, you get a flashback to an old mission one of the main characters carried out, and the first backstory-scene you get is the start of the mission, then the second scene is the middle of the mission, and then the third scene is the end of it - and in between that, the main plot in the present timeline is happening.
Ultimately, though, what suits your story is what should be your choice here, as @shazzbaa says. If the structure of your story requires that we know what happened in the protagonist's childhood at the beginning of the story, then do it as a prologue. To continue on the Pixar theme here, take UP. It begins with a 10-minute prologue describing practically the entire life of one of the main characters - and without it, the rest of the movie wouldn't make sense. We need to know why Carl is so insistent on keeping his house, why he feels he needs to make the ardous journey through the jungle, and why his personality is what it is - otherwise his insistence on all of these things would make no sense.