Hi I'm having problems with part c of this question

and I want to define fully the CDF. I know I have to intergrate the functions in turn

so the first bit between 0 and 2 is $\displaystyle \frac{1}{2}t^{2}$

and I begin doing the next part between 2 and 6 $\displaystyle \frac{1}{12}6t \frac{1}{2}t^{2}-10$ but in the mark scheme it's

$\displaystyle \frac{1}{24}6t -\frac{1}{2}t^{2}-12$

do you have to do somthing with the other limits first? I've missed a small step somwhere I think :\

Thanks