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

Which one of the following is the response y(t) of a causal LTI system described by
H(s) = (s + 1)
s² + 6s + 10

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

1. y(t) = e^{– 3t} sin t u(t)
2. y(t) = e^{– 3t(t – 1)} sin (t – 1) u(t – 1)
3. y(t) = sin (t – 1) u(t – 1)
4. None of these

Given

H(s) =	(s + 1)
	s² + 6s + 10

x(t) = e^–t u(t)
then

X(s) =	1
	s + 1

∴ Y(s) = H(s) X(s)
or

Y(s) =	(s + 1)	.	1
	s² + 6s + 10		(s + 1)

Y(s) =	1
	s² + 6s + 10

Y(s) =	1
	(s + 3)² + 1

(rearranging the terms)
or
y(t) = e^–3t sin t.u(t)
Hence, alternative (A) is the correct choice.