%% 
%%  Der Mathematiksatz mit LaTeX, 1. Auflage 2009
%% 
%%  Example 6-3-14 on page 100.
%% 
%%  Copyright (C) 2009 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 

\documentclass[]{ttctexa}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{355.65944pt}
\AtBeginDocument{\setlength\parindent{0pt}}
\setcounter{equation}{39}
\renewcommand\theequation{6.\arabic{equation}}
\StartShownPreambleCommands
\usepackage{amsmath}
\newcommand*\diff{\mathop{}\!\mathrm{d}}
\StopShownPreambleCommands
\begin{document}
\begin{align}
\begin{split}
A_1
  &= \left|\int_0^1 (f(x)-g(x))\diff x\right|+\left|\int_1^2 (g(x)-h(x))\diff x\right|\\
  &= \left|\int_0^1 (x^2-3x)\diff x\right|+\left|\int_1^2(x^2 -5x+6)\diff x\right|\\
  &= \left|\frac{x^3}{3}-\frac{3}{2}x^2\right|_0^1+\left|\frac{x^3}{3}
     -\frac{5}{2}x^2+6x\right|_1^2\\
  &= \left|\frac{1}{3}-\frac{3}{2}\right|+\left|\frac{8}{3}-\frac{20}{2}+12-\left(\frac{1}{3}
     -\frac{5}{2}+6\right)\right|\\
  &= \left|-\frac{7}{6}\right|+\left|\frac{28}{6}-\frac{23}{6}\right|=\frac{7}{6}
     +\frac{5}{6}=2\,\text{FE}
\end{split}
\end{align}
\end{document}