how to i download music from my iphone to my computer that I didnt purchase on Itunes?

My old Iphone is from 2011 and I recently damaged it. I filed an insurance claim and got a new Iphone. When I backed up my old Iphone, Itunes would only take the music I purchased on Itunes. How do I get the music that I didnt purchase on Itunes over to my new Iphone? Mind you, these music files are very old and were uploaded from computers I no longer have. There has to be a way. Please tell me how. I have over 750 songs I didnt purchase through Itunes and I have to erase my old Iphone and send it back to the insurance company. Please help!!!