Linebreak between \left and \right
if you want the parentheses of the same height, use \vphantom
and a combination of \left( ... \right. \\ \left. ... \right)
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
\left( \int_1^2 ba ba \mathrm da \right. \\
\left. ba ba ba \vphantom{\int_1^2} \right)% use height of \int
\end{split}
\end{equation}
\end{document}
Try this:
\documentclass{minimal}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
\left( ba ba ba \right. \\
\left. ba ba ba \right)
\end{split}
\end{equation}
\end{document}
You were right about the fact that the \left
and \right
should be on the same line.