Substitution to convert elliptic integral to standard form

[mercenarycor]

Homework Statement

[/B]
J(a, b, c;y)=∫_a^ydx/√((x-a)(x-b)(x-c)), let a<b<c

Homework Equations

f(θ, k)=∫₀^θdx/√(1-k²sin²(x)), k≤1

The Attempt at a Solution

This is an example from my study material, and I don't understand the first step they do.
Let x=a+(b-a)t, dx=(b-a)dt
Wait...what? Why? How did they come to that decision. I hope there's a logical reason, otherwise how can I apply this to my other problems? I keep running into "make an educated guess." Is this another guess?

 

[John Park]

I suggest you show a bit of unquestioning blind faith and try it.

 

[mercenarycor]

And that is how we discovered the new world!

 

[John Park]

And that is how we discovered the new world!

No shipwrecks or monstrous squid, I take it?

 

[mercenarycor]

Devoured by the Kraken, I'm afraid. Ended up dropping the course, going to spend the summer with Schaum's trying to build a better foundation for the math I need.