I have seen the following occur many times in calculus and have solved a couple of questions too of the type:
$$ \frac{d(f(x))}{d(g(x))} $$
i.e. differentiating one function wrt to another function.
And :
$$ \int_{a}^{b}f(x) d(g(x)) $$
what do both these mean, my questions in a line is what do these two mathematical statements mean, what are we doing when we are evaluating the above.
