Is music from apps other than iTunes restored in a back up?

I was grounded for 5 weeks with my iPhone 5c powered off. When I turned it back on everything was fine but it said it needed a software update. Then told me to connect to the computer. In doing so an alert popped up saying my phone needed to be reset to factory settings and then I could restore to the latest back up. I have music through a music app (1000+ songs) but its not iTunes. Will I get that music back or have to redownload it all?

If it was on your device, in the music app, it was backed up. No promises about any illegally gained apps. Those disappear

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