How to tell MathCAD something is constant

No need to tell Mathcad so, Mathcad's symbolic treats c as a constant (for MC's numeric c is velocity of light)

I guess you are puzzled as of the huge expression you get in evaluating that integral while you would have expected something like

But while Mathcad treats c as a constant it has to consider all possibilities, c could be -v1, it could be complex, etc.

So Mathcad gives you the results with a lot of if's to cope for every eventuality.

Your function has a vertical asymptote at v=-c, so the bounderies of your definite integral have to be both at the left or both at the right of -c, otherwise the integral would have to be infinity. Obviously c must not be -v1 or -v2 or you would get a divison by zero.

Replace c by a number and see that Mahcad still has some ifs, but less as with an unknown c.

You might try to use assume to get a more meaningful result. Unfortunately "assume" very often does not work as expected. E.g. "assume, -c<v1<v2" should do the job, but doesn't.

EDIT: Interestingly enough "assume, -c < v1" does the job - thats crazy!

In fact "simplify" would not be necessary here, typing it is just a reflex 😉