I need to express this function as a piecewise function. 
Now, it is not discontinuous so I'm lost. But my attempted solution is to break this into parts, first part is $f(t)=0, -\infty<t\leq a$, from $a \rightarrow b$, it is $f(t)=t, a\leq t \leq b$. The function here is$\frac{1}{b-a}$ because it increases by 1 from a to b. So the slope is assumed to be $\frac{1}{b-a}$. Am I on the right track?
