Sounds pretty interesting! I'm sure I'll learn that at universityYou definitely will.
Why do you have to change the bounds?Sometimes you have to switch the y and x functions.
Let's say you are to solve this integral
In it's current state it is unsolvable in elementary terms. There's no nice way to solve it for an exact answer. Some teachers might even tell you that it is completely unsolvable. The only way to solve it, is using a series and that can get really messy and you'd have to add a lot of numbers to get some result.
If you switch the bounds to being a dydx equation, it is actually really easy even to find an exact answer.