To integrate ∫(sin x + 2)dx, we can use the linearity of integration and the power rule of integration.
∫(sin x + 2)dx = ∫sin x dx + ∫2 dx
Using the power rule of integration, we have:
∫sin x dx = -cos x + C
where C is the constant of integration.
∫2 dx = 2x + C
Therefore,
∫(sin x + 2)dx = ∫sin x dx + ∫2 dx = (-cos x + C) + (2x + C) = -cos x + 2x + 2C
where C is the constant of integration.
So, the correct option is: -cos x + 2x + K.