In my numerical analysis class i was sick during the class they did the Cubic Spline and I'm getting confused.

Question: Determine the FREE cubic spline S that interpolates the data f(0)=0, f(1)=1 and f(2)=2.

So far from following the examples in the book i have:

S(x)={S_0(x)=a_0+b_o(x-0)+c_0(x-0)^2+d_0(x-0)^3 0<=x<=1

{S_1(x)=a_1+b_1(x-1)+c_1(x-1)^2+d_1(x-1)^3 1<=x<=2

Like i said I was following an example in the book and its not very clear so I'm not even sure how i got that far. I know i have to form a matrix but I have no clue how...the answer in the back of the books says : S(x)=x on [0,2]

If someone can please help maybe to explain the steps and then I could follow suit. And i'm pretty sure it belongs in this category if not please redirect me. Thanks so much.