Let's say I have a forest of x trees (a bunch of disconnected trees). How many edges must be added to convert the forest into a single, contiguous tree?
Wouldn't it just be x-1 edges?
The problem also states that the trees have $y_1, y_2, ..., y_x$ vertices, respectively, and I don't understand why this information is relevant.
Am I misinterpreting something?
If you're unconvinced, try a proof by induction. Start with the case where $x=2$. Then assume it works when you have $n$ trees and look at what happens when you have $n+1$ trees.