You asked,
Is there an efficient way to set all the integration limits in the document to \textstyle?
When TeX is in displaymath mode, \int produces a "large" integral symbol and the upper and lower limits of integration are typeset in scriptstyle. What you're encountering is that the numerators and denominators inside these limits are typeset in scriptscriptstyle if \frac is used.
To change this default behavior globally, i.e., to switch from scriptstyle to textstyle in the limits of integration on a document-wide basis, would require major surgery on TeX's math innards and is not to be undertaken lightly. And I would hate to call such coding efficient. Moreover, you will probably not like the resulting look if the limits contain simple numbers and letters (since these will now be set in textstyle, i.e., the same size as applies for \sin x\,\mathrm{d}x.
You could use \tfrac explicitly -- \tfrac is short for \textstyle\frac-- to get scriptsize- rather than scriptscriptsize-sized numerator and denominator terms; the resulting look is also shown in @Bernard's earlier answer. Alternatively, you could use "inline-style" fraction notation, i.e., write \pi/4 and \pi/2 in the limits; these terms will be set in scriptstyle automatically.

\documentclass{article}
\usepackage{amsmath} % for \text and \tfrac macros
\begin{document}
\[
\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\sin x\,\mathrm{d}x % \frac
\quad\text{vs.}\quad
\int_{\tfrac{\pi}{4}}^{\tfrac{\pi}{2}}\sin x\,\mathrm{d}x % \tfrac
\quad\text{vs.}\quad
\int_{\pi/4}^{\pi/2}\sin x\,\mathrm{d}x % inline-style
\]
\end{document}
\documentclassto\end{document}) so it allows us to just copy your code to start working rather than writing it ourselves ;) – Manuel Jul 18 '14 at 10:17\tfrac, provided you have\usepackage{amsmath}; but the best is to use the slashed form:\int_{\pi/4}^{\pi/2}– egreg Jul 18 '14 at 10:17\tfracin case, if you set all the sub/superscripts in textstyle\int_0^1 fwould be definetly ugly with0and1of the same height off. – Manuel Jul 18 '14 at 11:51