I'm not sure how to begin/approach/do this problem or apply the theorem.
You must deduce an equation for f(x) from the given graph. It is the graph of sin(x), shifted 1 place along positive x, and shifted 2 placed along positive y, and squished/expanded by a factor of... something! You must then inject that equation into the integral:
And carry out the integration to get a function in x for g(x).