Dummy Variables and variables that change a funtion I am reading notes for my Calculus 2 class and am confused why these two functions are not equivalent
"
$x$ is not a dummy variable, for example,
$$\int 2xdx = x^2+C$$
and 
$$\int 2tdt = t^2 + C$$
are functions of different variables, so
they are not equal. 
"
Is it because the arbitrary C's can be different?

Either $x$ or $t$ is just a token representing numbers, so they are equivalent.
Let's take the expression $x+1$ (or $t+1$) for instance: Letting $x=1.5$ is equivalent to letting $t=1.5$, because both of them make the expression evaluate to $1.5+1=2.5$.
