For part a, there is a branch point at s=-1 and a simple pole at s=0. u can take a cut from -1 to -infinity and draw a bromwich contour.

For part b is where it gets tricking and I need help, since it is Sqrt(s+1), there will be two Reimann sheets, in part a) we are assuming a reimann sheet from -pi to pi,

but for part b, we can look at the mapping of reimann sheet of pi to 3pi onto the complex plane. Hence, need to find the singularities and branch points on that reimann sheet.

for part c, need to refer to the bromwich curve and break it up in parts to find the inversion formula.

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