You mention that very specific requirements for the document - only two pages, and a two-column format. The following minimal example duplicates this using the multicol package. It allows multiple column document format via the multicols environment that takes a mandatory argument:
\begin{multicols}{<n>}
...
\end{multicols}
This is an option in lieu of specifying a twocolumn document class option. As such, specifying your first image before starting the multicols environment, and specifying the second image after produces the desired result. The first image is still specified within a figure float with a float specifier of [b] (for bottom placement) while the last figure has a float specifier of [t] (for top placement):

\documentclass{article}
\usepackage{multicol}% http://ctan.org/pkg/multicol
\usepackage[demo]{graphicx}% http://ctan.org/pkg/graphicx
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\begin{document}
\begin{figure}[b]
\centering
\includegraphics{figure1}
\caption{This is the first figure}
\end{figure}
\begin{multicols}{2}
\lipsum[1-7]
\end{multicols}
\begin{figure}[t]
\centering
\includegraphics{figure2}
\caption{This is the second figure}
\end{figure}
\end{document}
In the above example, graphicx is loaded with the demo package option which replaces all images with a 150pt x 100pt black rectangle (for compatibility reason). You should remove this for your document. Also, lipsum was used to generate dummy text.