The OP has the definition of x(t).

Incorrect for this problem. It is defined byCan you confirm that x(t) is defined as being equal to 1 for 0<=t<=1, zero for 1<t<2 and 2 for t>=2 ?

At least, that's my interpretation of this line of the OP:

where x(t) = 1, 0≤t≤1;

2, t≥2;

0 elsewhere