Old English unbindan, "to free from binding," from un- (2) "opposite of, reverse" + bind (v.). Similar formation in Old Frisian unbinda, German entbinden, Dutch ontbinden. Literal and figurative senses both present in Old English.
Suæ huæt ðu unbindes ofer eorðu bið unbunden in heofnum. [Lindisfarne Gospels, Matthew xvi.19]
Unbound is from Old English unbunden, in literal sense. Figurative sense first attested late 14c.; of books from 1540s.