Laplace transform of averaging operator
Here's the outline of the argument, feel free to fill in the details.

The averaging operator is like a convolution with a "square" pulse of height $1/T_s$ supported on the interval $[-T_s/2, T_s/2]$. 

You can express the square pulse as a sum of two heaviside step functions. 

Finally, recall the Laplace transform of a step function $\mathcal{L} \{H(t-T_s/2)\}(s) = \frac{e^{-sT_s/2}}{s}.$