It's not framed the responsible for this change in the math symbols, but MnSymbol.
Here's the example:
\documentclass{article}
\usepackage{MnSymbol}
\begin{document}
bla bla bla $\cap_{i\in I} X_i.$
\end{document}

Don't trust in advice (even if it's from this site) telling you to use the package just because it provides some symbol you need, because this package changes all math symbols to shapes that are thought to blend with the Minion font and are definitely out of place with Computer Modern (see the ugly \in).
Look at Importing a Single Symbol From a Different Font for importing just the symbols you need.
By the way, the correct way to input that formula is
$\bigcap_{i\in I}X_{i}$.
Note \bigcap and the full stop outside the formula.
framed.styto make sure the version used is still the same on ctan. (it is.) – barbara beeton Feb 28 '15 at 18:07framed.styin the standard distribution will not change the fonts. please add\listfilesto your example, uncomment theframedline and then if it still changes the font add the full log to your question, so we can see what it's done. – David Carlisle Feb 28 '15 at 21:58