(Probably a Silly Question) Definite Integral With Respect to Independent Variable?

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I was trying to understand how to evaluate and indefinite integral of a function with respect to a independent variable and after reading through this Integrate a function with respect to a different variable?, I learned that we can treat all terms independent of the variable we are integrating with respect to as constants.

Then I just thought to myself, "huh that's interesting, I wonder how this changes when it's a definite integral?". And I found this post but only got confused by trying to understand what they we're talking about. Now I just think this is a silly question because there isn't much out there online about it, but I was curious if someone could explain to me why it was a silly question? Thanks.