Which one the following is the response y(t) of a causal

Which one the following is the response y(t) of a causal LTI system described by
H(s) = (s + 1)
s² + 2s + 2

for a given input x(t) = e^{– t} .u(t)?

1. y(t) = e^{– t} sin t.u(t)
2. y(t) = e^{– (t – 1)} sin (t – 1).u(t – 1)
3. y(t) = sin (t – 1) u(t – 1)
4. y(t) = e^{– t} cos tu(t)

Given

H (s) =	(s + 1)
	s² + 25 + 2

if x(t) = e^–tu(t)
then

X(s) =	1
	s + 1

Now,
Y(s) = H(s).X(s)

or Y(s) =	(s + 1)	.	(s + 1)
	s² + 25 + 2		(s + 1)

or Y(s) =	1
	(s + 1)² + 1

y(t) = e^–t.sin t.u(t)
Hence, alternative (A) is the correct choice.

H(s) =	(s + 1)
	s² + 2s + 2