Area under 1/x and the natural logarithm function

Thinking about the area under the y=1/x curve. This case is usually not considered when first meeting definite integrals.
Drag the slider bar and note the values of the area under the curve y=1/x between x=1 and x=2,3,... You might notice that the area to the left of x=3 added to the area to the left of x=2 gives the area to the left of x=6. Can you find any other similar patterns? What does this tell you about the nature of the area function? And for what value of a is the area equal to 1? Why is this important?