Hey, first post.

I was looking through the textbook and their rules for the integral of a function done to a linear function, eg

or

or

all seemed to fit the general case

Simply, am I right?

If so, is this a general rule that just isn't explained in high school?

If not, could you please help me as to where I've gone wrong, or are there any amendments that would put me on the right track?

I'm really enthusiastic about this sort of stuff, so any help/advice is great!