Need help on a couple of M1 questions

When integrating velocity or acceleration, there is a constant. How do you find the constant? I was trying to do question 6 (http://www.ocr.org.uk/Images/59970-question-paper-unit-4728-mechanics-1.pdf) and completely flopped the whole question. I tried understanding what the mark scheme said but it kind of got out of hand so can anyone walk me through this question and question 7

You are told in question 6 that the particle passes through O (i.e. where its displacement from O is 0) when t = 2. You can use these initial conditions to find the value of the constant in the first part.

Ohh I didn't realize that. Thanks for that.
Still not sure on how to answer questions like 6ii where the particle moves forward and backwards. How do you know if something is changing direction? Is it when its displace goes from positive to a negative and vice versa? But then how would you go on about doing this question?