The graph of \(y = a + b \sin x\) is a vertically shifted sine wave.

The midline of the sine wave is at \(y = 1\), which indicates that \(a = 1\).

The amplitude of the sine wave is the distance from the midline to the maximum or minimum point. The maximum value is \(3\) and the minimum value is \(-1\), so the amplitude is \(\frac{3 - 1}{2} = 2\).

Thus, \(b = 2\).