I was pretty bored in my 7th period today (student assistant, but the teacher never has me do anything), so I started messing around with the graphs, found a few parent functions, and made this:
I used the calc option to find the integral (option 7, shades the graph for area).
The functions (I stored (π/2 - Y) in A, where Y was the y-value of the second function at π/2).
The x-min is -(47π)/24, the x-max is (47π)/24, the y-min is -(31π)/24 - 1, and the y-max is (31π)/24 - 1
It took about 20 minutes to completely put together.