How did Prospero and Miranda end up on the island years before the present action of the play?

Prospero was once the Duke of Milan. His brother, Antonio, usurped his position while Prospero was immersed in "secret studies". After taking his title and lands, Antonio plotted to take both Prospero and Miranda's lives, but his plot didn't turn out as planned because the men charged with secretly killing the two couldn't do it...... thus, they set them adrift in a broken down ship. Miranda and Prospero survived and landed on the island where they presently live.