As Vikas says, it appears from your version number that you are using SDL Tridion 2013 SP1 but not HR1.
I don't have an instance with HR1 installed on, but if previous versions of Tridion are anything to go by, then the if HR1 is installed then this should display in the 'About' page.
For example, please see the screenshot below (from @Pankaj's answer here: https://tridion.stackexchange.com/a/3074/71).
Alternatively, if you can find out the exact DLL and JAR file version numbers that are expected for HR1 (Nuno or someone 'internal' may know these) then you can use the tools in Dominic's answer to "Find the version build numbers for SDL Tridion 2013 sp1" to find the JAR file and DLL file versions on your server.
You will need to keep track of additional hotfixes installed yourself. There are three common techniques for this:
- As Vikas mentions, you could do this using the Hotfix Manager tool from SDL Tridion World.
- You could use a shared spreadsheet to log all the details of any hotfixes applied, or
- You could store all hotfixes that have been applied in a shared folder. However, this would not give the order in which they have been applied!