Properties of Definite Integrals

This is the geometric interpretation of the definite integral property Spend 10 minutes to think about the questions that follow.
1.) Geometrically, how does the slider change the function f(x)? 2.) How does the equation for g(x) relate to the equation for f(x)? 3.) How does the area under g(x) from x=0 to x=4 relate to the area under f(x)? 4.) What did you notice when k =0? 5.) Can you think of a slogan for the property ?