I found the above page on the Internet which might help you to relate your problem to the relevant integration.
Looking at it from a purely mathematical viewpoint, and considering the amount of information you have been given, we need to relate some factors. We start with entropy of C₂H₅OH as S₁=160.7 J/°K at 298°K. We need to find S₂ at 348°K, which is 50°K higher. We have the heat capacity at constant pressure C(p)=111.46J/°K. Now, if this was linear we would simply multiply the heat capacity by 50 (ignoring the absolute temperature of the alcohol) and add (or subtract) it from 160.7 to get the required entropy S₂. But from your question and from the internet page the change is not linear but logarithmic. I’m not sure if the gas constant R comes into this but, assuming for a moment that it doesn’t, then I think that the clue is S₂-S₁=C(p)ln(348/298). So we would get S₂=160.7+111.46ln(348/298)=177.99 J/°K. I hope this helps.