Geometrical Interpretation of Indefinite Integration

An indefinite integral of a function always gives a family of curves and these curves may not be similar. The family of curve is created due to placement of a constant at the integration. Thus, if integration of F(x) is f(x)+c, then we get a family of curve f(x).

Now, if any line parallel to X axis is drawn, it cuts all members of this family at points, say, A, B, C, D, and so on, and the tangents drawn at all such points of intersection are parallel. See the attached PPT video.