Captions not directly below figure in minipage environment

Question

So I wanted to show two pictures side by side, put captions below them and then replace some text inside.

This is what I have done:

\documentclass[a4paper,12pt]{article}


\usepackage{fullpage}
\usepackage[utf8]{inputenc}
\usepackage{amssymb, amsmath, amsthm}
\usepackage{psfrag, graphicx}

\begin{document}
\begin{figure}
\centering
\begin{minipage}[c]{.5\textwidth}
  \includegraphics[width=1\linewidth]{convplot1}
  \caption{first figure}
  \label{fig:1}
\end{minipage}%
\begin{minipage}[c]{.5\textwidth}
  \includegraphics[width=1\linewidth]{convplot2}
  \caption{second figure}
  \label{fig:2}
\end{minipage}
\end{figure}


\end{document}

I would like to have the captions show up right below, while using the minipage environment, but what it actually gives me is this:

I am not quite sure how to fix it, so any help is greatly appreciated!