/Library/Extensions/PromiseSTEX.kext

I have checked them. There is no PromiseSTEX.kext listed.

you can just delete that .kext file

You need to locate this extension in the location shown, select it, CTRL- or RIGHT-click and click on Move to Trash. Restart the computer. You may need to do this twice.

Not quite. You have to restart the computer. If you don't, the the extensions cache will not be rebuilt.

Your OS X installation is corrupt. Don't delete anything.

If you don't already have a current backup, back up all data, then reinstall the OS.* You don't need to erase the startup volume, and you won't need the backup unless something goes wrong. If the system was upgraded from an older version of OS X, you may need the Apple ID and password you used.

There are ways to back up a computer that isn't fully functional. Ask if you need guidance.

If you installed the Java runtime distributed by Apple and still need it, you'll have to reinstall it. The same goes for Xcode. All other data will be preserved.

*The linked support article refers to OS X 10.10 ("Yosemite"), but the procedure is the same for OS X 10.7 ("Lion") and later.

Your installation is NOT corrupt. You need not backup and reinstall OS X. At least not yet. The poster who states this is incorrect.

The file referred to in the alert is a built-in component of OS X, as you can easily verify by doing a simple web search. If it was "installed improperly," then by definition the installation is corrupt. Never delete built-in components of the operating system for any reason. Dangerous misinformation is rife on this site.

Not evident in Yosemite on my systems. You are obviously disseminating dangerous misinformation. There is no evidence of that .kext file in Mavericks or Mountain Lion. If that extension is part of OS X, I sure can't find it. More likely it was installed by a Promise Technology product.

Better look again, Kappy. That kext IS part of OS X. I've checked three of my Macs, and they all show this item.