Integrating algebraic functions The function $y = f(x)$, restricted on the domain $ 0 < x < 1$ and satisfying
$$y^{5}+y^{4} + x = 0,$$
seems to be well-defined and smooth. So how does one integrate this thing? That is, what is $\int_{0}^{1} f(x) dx$? 
Of course, one can use Newton's method to approximate $f(x)$ for any given value of $x$ and numerically integrate the result. But this feels uninspiring. So I was wondering if there is a general "trick" or insight to integrating algebraic functions.

This is @Teri: 's idea.
Given 
$$F(y) + x =0$$
differentiate and get 
$$F'(y)\, d y + d x = 0$$
and so $$y\, d x = - y\, F'(y)\, d y$$ and now integrate:
$$\int_a^b y\, d x  = \int_{y(a)}^{y(b)}-y F'(y) dy $$
