Well, some areas you might be asked to find are, say, under arcsine or arccos graphed [sin^(-1)x etc ] or log graphs. To find the area here them you find the area to the y-axis and subtract it from the whole rectangle, if you kinda get me. You can integrate sinx and cosx so the area will be the whole area for the upper limit to both axes - the area you can integrate. Hard to explain, but you'll get it.
Another type of integration often occurs when they give you something particularly nasty or muddled to differentiate (usually a 'show' question) and then the next part of the question has the function as a slight variation of the derivative so you know what the integral would be (what you initially differentiated but amended)
Basic Example.
i)(d/dx) x.lnx-x
=x×1/x+1×lnx - 1
=1-1+lnx
=lnx
ii) hence find the area covered by a particle from a to be seconds if it's velocity is given by ln2x where x is seconds.
You couldn't previously integrate ln2x but now you know what it came from so you can. These only occur every so often but are good to know. If you do maths in the future then it's good to note weird differentiations especially for hard things like arctan quickly.
