I do not agree with the "answer". assuming that the question is asking for total distance traveled from t = 0 to t = 3 ...

particle is moving left from t = 0 to t = 5/4 sec

distance traveled in that interval = (1/2)(5/4)(5) = 25/8 m

from t = 5/4 to t = 3 sec, the particle moves to the right ...

distance traveled in that interval = (1/2)(7/4)(7) = 48/8 m

total distance traveled = 25/8 + 49/8 = 74/8 = 9.25 m

total distance can also can be calculated by the definite integral ...