Does integration give area between graph and x axis?

[CAH]

Does integrating find the area between the curve and x-axis (regarless of it being a smile/frown or any other graph)?
I've heard people say its the area UNDER a curve...
but then how would you even get a definit answer surely it may be infinite if there's no restrictions?

Thanks

 

[jbriggs444]

When people call it the area "under a curve", there is still the implicit assumption that it is above the x axis.

For a definite integral from a to b, you would be calculating the area of a region bounded as follows:

On the left by the vertical line defined by x=a
On the right by the vertical line defined by x=b
On the bottom by the horizontal line defined by y=0
On the top by the graph of the function.

 

[jk22]

Note that if the curve is below the x-axis then this area is counted with a minus sign

 

[CAH]

If it's below the x-axis is it calculating the area above the curve, between the curve and the x-axis above it

 

[jbriggs444]

As jk22 pointed out, the areas of any regions where the graph is below the x-axis count as subtractions from the total area, not as additions. If the entire graph is below the x-axis then the entire area will be counted as negative.

But yes, other than this concern about the sign of the result, it is calculating the area above the graph and below the x axis.