as Delta t i.e impulse function is defined as delta (t)=( limit a tends to 0)1/a, for all t=a, where a~0 ; or for all t it is Zero.
so the integration will become {for a Limit tends to 0} ::Integration 0----a [(1/a)*cos(3t/2)]dt.
after solving integration it will reduce to
Limit a tends to 0 [1/a*{2/3*Sin(3a/2)}]
after rearrangement
Limit a tends to 0 [Sin(3a/2)/(3a/2)]
after applying limit final answer will come one(1).
I.e. first option
after solving