Framed text set by CSS

Things I have tried

Without div tag:

Let $f(x)$ be continuous on $[a,\infty)$. We define $\displaystyle\int_{a}^{\infty} f(x), dx$ to be $\displaystyle\lim\limits_{t\rightarrow \infty} \int_{a}^{t} f(x), dx$.

With div tag:

Definition of Improper Integral Let $f(x)$ be continuous on $[a,\infty)$. We define $\displaystyle\int_{a}^{\infty} f(x)\, dx$ to be $\displaystyle\lim\limits_{t\rightarrow \infty} \int_{a}^{t} f(x)\, dx$.

What I’m trying to do

I attempted to surround my text with a HTML div tag. I then want to use CSS to add borders, etc. However, inside a div tag, the LaTeX is not processed.

Not sure if this is something you are looking for, but the example below can be made with the plugin Admonition:

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