Analysis: Deduce f ′ (x) = cosx+1≥ 0, and get that the function f(x)=sinx+x- 1 is a monotonic increasing function on R, and the zero point of f(x)=sinx+x- 1 is on the right side of the origin, thus getting the function f (.

Solution: solution: ∫f(x)= sinx+x- 1.

∴f'(x)=cosx+ 1≥0, ∴ function f(x)=sinx+x- 1 is a monotone increasing function on R,

And the zero point of f(x)=sinx+x- 1 is on the right side of the origin, as shown in the figure.

The image with function f(x)=sinx+x- 1 does not pass through the second quadrant.

So choose B.

Comments: This small topic mainly examines the application of monotonicity of functions, the images of sine functions, the images of functions and other basic knowledge, the ability to solve operations, and the idea of combining numbers with shapes, which belongs to basic topics.