What is the difference between mindfulness and detachment? From Mindfulness:


  Mindfulness is the psychological process of bringing one's attention to experiences occurring in the present moment, which one can develop through the practice of meditation and through other training. Followers of Buddhist teachings utilize mindfulness to develop self-knowledge and wisdom that gradually lead to what is described as enlightenment or the complete freedom from suffering.


From Detachment:


  Detachment, also expressed as non-attachment, is a state in which a person overcomes his or her attachment to desire for things, people or concepts of the world and thus attains a heightened perspective. It is considered a wise virtue and is promoted in various Eastern religions, such as Taoism and Buddhism. 


I see that the two terms are very related, but I'd like to understand more about the differences and the interactions between the two. As in my understanding, the answer to the question mindfulness thinking about future and past? is that as long as one is detached to the past and the future, one can mindfully examine them. Is that correct?
'Mindfulness' means 'to remember' to apply/practise the Buddhist teachings. It does not mean 'bringing one's attention to experiences occurring in the present moment' (as written by a person in Wikipedia). 

For example, if I wish to stalk and assassinate (murder) another person using a rifle, I must meticulously bringing my attention to experiences occurring in the present moment. Yet murdering a person in the present moment is not practising the Buddhist teachings. 

In summary, for the 'trainee' of the higher path, the mind must continuously remember to not attach to any experience. Therefore, to practise non-attachment requires mindfulness, as written in the suttas: 


  His mindfulness... is maintained to the extent of knowledge &amp; remembrance. And he remains independent, not clinging to anything in
  the world. 
  
  MN 10