I'm dealing with a function that can be written in all of the following forms:
$$f(x) = \frac{x + |x|}{2} \\ = x\ \Theta(x) \\ = \int_{-\infty}^x \Theta(y) \operatorname{d}y,$$
where $\Theta(x)$ is the standard unit step (Heaviside) function. Does the function $f(x)$ have a special name?