DSE 2014 Macro Question

[cheesecake]

I am trying to understand Amit sir's solution for the macro problem of DSE 2014. This is the labour supply question. I understand that we differentiate utility with respect to labour hours and then equate to zero to maximize utility of the laborer. This gives the first part of the labour supply curve.
But how do we get the second part? Why is l = 1? Someone please explain.. i can't move on to the next question otherwise

[throwaway]

Think of it this way : supposing w_t was given as 4, and δ was given as 2. What would you get the labour supply as, if you used the setting derivative = 0 method? It would exceed 1 - which is why you need to consider two cases. a) when w_t is less than delta (normal method) and b) when w_t is more than delta, in which case you would provide as much labour as possible, which is 1.