@tomleslie Thx for your answer

@Kitonum 

Thank you for the reply.

I now see what the problem is, I forgot to write the command with(plots) :D

GOD bless U

@acer thank you very much for this upload document, it is very appreciated.

I was looking for this command to get the result in the form I got in my solution by hand :))

GOD bless U

@tomleslie thank you for your feedback.
somehow I can not see the conceptual problem, but I have given the integral an upper and lower value x*(x^2-1)^5 and I have also given x a value for (x^2-1)^6/12 and the two results corespondce together.

You wrote "Which of these (indefinite)  integrations gives rise to the constant term 1/12" is it possible for you to explain this :))
 

@Axel Vogt 

Thank you for reminding me of this :))