# Does integration give area between graph and x axis?

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 theres no restrictions?

Thanks

jbriggs444
Homework Helper
2019 Award
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.

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

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