Given that
$$L\left[ {f\left( t \right)} \right] = {{s + 2} \over {{s^2} + 1}},L\left[ {g\left( t \right)} \right] = {{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s + 2} \right)}},$$        $$h\left( t \right) = \int\limits_0^t {f\left( \tau \right)} g\left( {t - \tau } \right)d\tau $$
L[h(t)] is

A. $${{{s^2} + 1} \over {s + 3}}$$

B. $${1 \over {s + 3}}$$

C. $${{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s + 2} \right)}} + {{s + 2} \over {{s^2} + 1}}$$

D. None of the above

Answer: Option B