I would like to use multline
environment, but in that way that centered part be left aligned. With multline centered part is centered, and I would like if we can somehow to aligned it to the left (but to stay centered). And of course, if this is possible to do with align
environment (but that first line is flush to left and last to the right), that is better for me, because than I can label arbitrary equations (because with multline I can label just last one equation). I hope I didn't confuse you too much.
Here you MWE
\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{lipsum}
\begin{document}
\lipsum[1]
\begin{multline}
A = \lim _{n\rightarrow \infty }\Delta x\left( a^{2}+\left( a^{2}+2a\Delta x
+\left( \Delta x\right) ^{2}\right)\right.\\
+\left( a^{2}+2\cdot 2a\Delta x+2^{2}\left( \Delta x\right) ^{2}\right)\\
+\left( a^{2}+2\cdot 3a\Delta x+3^{2}\left( \Delta x\right) ^{2}\right)\\
+ \ldots\\
\left.+\left( a^{2}+2\cdot (n-1)a\Delta x +(n-1)^{2}\left( \Delta x\right) ^{2}\right) \right)\\
= \frac{1}{3}\left( b^{3}-a^{3}\right) + \text{something}
\end{multline}
\lipsum[2]
\end{document}