Final answer:
The integral of ∫(cos(x) - 1) dx is evaluated by integrating each term separately, resulting in sin(x) - x + c, where c is the constant of integration.
Step-by-step explanation:
To evaluate the integral ∫(cos(x) - 1) dx, we need to integrate each term separately. The integral of cos(x) is sin(x), since the derivative of sin(x) is cos(x). The integral of -1 is -x, because the derivative of -x with respect to x is -1. After integrating both terms, we add the constant of integration c.
Therefore, the integral is:
∫(cos(x) - 1) dx = ∫cos(x) dx - ∫1 dx = sin(x) - x + c