What is meant when someone write $d(e^{-t^2}y)$ or any kind of function for that matter inside those brackets? I read somewhere that it is a total derivative? What is it? And what gives us an ability to then write (as an example):
$$\int_0^x d(e^{-t^2}y) = e^{-x^2}y - y $$ without actually specifying what we are integrating with respect to? And why can we do the above anyway?