The research into this topic is ongoing and the conclusion so far is that exercise can be very good for our mental help for a whole host of reasons. It can reduce stress, for example, and improves mood by releasing hormones called endorphins. It sometimes provides a nice distraction from whatever issues you are dealing with in your day-to-day life, plus it gives a focus and a goal for the day that can be really good for our mental health.
I recently wrote about this in my blog '5 ways exercise is good for the mind' so I'd recommend reading this if you want to know a little more about the research involved in this topic.
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