Beginner Integration: Intg'g Arbitrary Funcs: Area B/w Intersects

[Jake Minneman]

http://www.google.com/imgres?imgurl=http://www.msstate.edu/dept/abelc/math/integral_area.png&imgrefurl=http://www.msstate.edu/dept/abelc/math/integrals.html&usg=__eYIUnirereMFeYOxrfWSZ22D6MU=&h=599&w=684&sz=24&hl=en&start=0&sig2=5Xoc8E51gnWrd4Z6mnluLA&zoom=1&tbnid=ofF46QkIclKjQM:&tbnh=142&tbnw=162&ei=7VfZTbHvDdO_gQfe49lX&prev=/search%3Fq%3Ddefinition%2Bof%2Ban%2Bintegral%26um%3D1%26hl%3Den%26sa%3DN%26biw%3D1416%26bih%3D1071%26tbm%3Disch&um=1&itbs=1&iact=rc&dur=520&sqi=2&page=1&ndsp=44&ved=1t:429,r:22,s:0&tx=106&ty=50
I know this to be the definition of an integral in the form of
$$∫a to b f(x)dx=F(b)-F(a)$$
But what if, however, there were another arbitrary function intersecting the function in the picture twice each with a curved nature. For example the function sin(x) is it possible buy using integration to calculate the area in between the two intersection points and the x-axis
Kind of a strange question, and its not very to the point ask questions if you do not understand my wording.

 

[tiny-tim]

Hi Jake!

You mean the area under the lower of two intersecting functions?

Just do two integrations, one for the first function when it's underneath, the other for the second function when it's underneath.

 

[Jake Minneman]

Yes exactly, thank you very much.