# Flush left and right in a same equation environment

I would like to do something like

\begin{align*}
\flushleft A(x) = \\
\flushright B(x) \\
\flushright + C(x)
\end{align*}

My problem is to set a nice layout for this long equation, where I have to cut a sum in multiple lines.

Environment multline of package amsmath has \shoveleft and \shoveright for flush right and left:

\documentclass[a5paper]{article}
\usepackage{amsmath}
\begin{document}
\begin{multline*}
% First line is flush left
A(x) = \\
% Move to the right, default is centered
\shoveright{B(x)} \\
% Last line is flush right
+ C(x)
\end{multline*}
\end{document}

## Variation

Alignment point is set for the relational operators. The parts left of the less signs are right aligned, the parts right of the alignment point is left aligned:

\documentclass[a5paper]{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
A(x) & \leq \\
B(x) \\
{} + C(x) & < 3 \epsilon
\end{align*}
\end{document}

I'd avoid “flush right”:

\documentclass{article}
\usepackage{amsmath}

\newcommand\diff{\mathop{}\!\mathrm{d}}

\begin{document}

\begin{align*}
& \biggl|
\int_{[0,1]^n}
f\Bigl(\frac{x_1+\dots+x_n}{n}\Bigr)
\diff x_1 \dots \diff x_n
-f(1/2)
\biggr|
\\
\int_{[0,1]^n}
\biggl|
(f-p)\Bigl(\frac{x_1+\dots+x_n}{n}\Bigr)
\biggr|
\diff x_1 \dots \diff x_n
\\
\\