Local extrema of an odd function with a sine term and the area enclosed with the segment to the minimum point

Let \(\mathrm{g}(x)=x^3-5x+4\sin x\), where \(x\in\mathbb{R}\).

On the graph of \(y=\mathrm{g}(x)\), the point \(A\) is a local maximum and the point \(B\) is a local minimum. The origin \(O\) lies on the line through \(A\) and \(B\).

The region \(R\), labelled in the diagram, lies between the graph and the line segment \([OB]\).

1. Find the coordinates of \(A\) and of \(B\).[2]
2. Find the area of \(R\).[5]