Linear First Order ODE/dy = f(x) dx

Theorem
Let $f: \R \to \R$ be an integrable real function.

The linear first order ODE:
 * $(1): \quad \dfrac {\d y} {\d x} = \map f x$

has the general solution:
 * $y = \displaystyle \int \map f x \rd x + C$

where $\displaystyle \int \map f x \rd x$ denotes the primitive of $f$.