On this site I've found a formula for calculating the $x, y$ coordinates for a body throwed by an angle to a horizon.
It looks like this:
$$x(t) = V_0 t \cos(\alpha); $$ $$y(t) = V_0 t \sin(\alpha) - gt^2/2; $$
It's clear to me that term $(g t^2)/2$ was received by the integration of $gt \, dt$.
But, I don't understand, why didn't we integrate $V_0 t \sin(\alpha)$ part of the equation?
Why do we integrate only $gt$ term?