We’ve had a couple of users who’ve had problems running MyEclipse on the OS X release 10.9 (or “Mavericks”). It seems as though upgrading to Mavericks can affect the Java installation in some way (for one user, Java’s certificate file appeared to be erased).
If you get an integrity check error when trying to run or install MyEclipse, after upgrading to Mavericks, reinstalling Java (or installing the latest release of the JDK) should fix it. Reinstall MyEclipse, if necessary, after reinstalling Java.
If the above fix doesn’t work for you, please raise a new topic on the appropriate forum.