Given that h(t) = 10e^-10u(t), and e(t) = sin10t.u(t), the Laplace transform of the signal $$f\left( t \right) = \int\limits_{\tau = 0}^t {h\left( {t - \tau } \right)e\left( \tau \right)d\tau } $$      is given by

A. $$\frac{{10}}{{\left( {s + 10} \right)\left( {{s^2} + 100} \right)}}$$

B. $$\frac{{10\left( {s + 10} \right)}}{{\left( {{s^2} + 100} \right)}}$$

C. $$\frac{{100}}{{\left( {s + 10} \right)\left( {{s^2} + 100} \right)}}$$

D. $$\frac{1}{{\left( {s + 10} \right)\left( {{s^2} + 100} \right)}}$$

Answer: Option C