From my experience and from reading what has worked for others.....
If you are trying to lose weight, then no. If you are burning calories with exercise in order to help create a calorie deficit and lose weight, then it makes no sense to eat back what you just sweated off.
However, if you have hit a plateau in weight loss then upping your calories may help break it.
(This is assuming you are talking about normal amounts of exercise--not someone who goes out and lifts heavy weights for 4 hours in the gym every day, or is training for the Iron Man competition!

)
If you are only interested in maintaining your weight, then yes you should be eating more calories if you have become more active.
Hope this helps.