Please show me the solution by adding some explanations?
You do appreciate that it is rather fearsome? http://m.wolframalpha.com/input/?i=integral+t%2F%28t%5E6%2B5%29&x=0&y=0
The integrand, f(t) = t/(t6 + 5), is an odd function. That is f(-t) = -f(t), so the integral between -3.7 and 0 exactly cancels the integral between 0 and +3.7, with the overall result of the integration being zero.
You can see this in the following image: