How do AES and DES ensure data integrity? I have been trying to study for cryptographic symmetric algorithms (AES,DES) and came up with a question whether these two on their own ensure integrity (i.e data has not been altered). Do these two need message digests in order to ensure it?  

I have also seen this paper, but it does not show 'how' these two algorithms ensure integrity.
Answer to your question title: they don't.

Answer to your inline question: yes (or something similar to it).

Longer answer: 

Both DES and AES are examples of block ciphers, and block ciphers do not have any inherent integrity protection. Thus, in order to also ensure integrity you would need to add something more, for example a message authentication code (MAC) or a digital signature. 

However, note that you would probably never want to combine DES and AES directly with, say, a MAC. Instead, you would want to use DES and AES in a dedicated mode-of-operation that provides both confidentiality and integrity for you (which together is called authenticated encryption).