How do I sketch the region whose area is given by the definite interval?

Question

Then how do I use a geometric formula to evaluate the integral (a>0, r>0)?

Answer 1

what is a, and what is r?

check the limits, that delimits how x varies,
then sketch the graph of the function, and
the region is simply whatever is between the graph and the x-axis

Answer 2

Unless you know what the particular function in question is, it's hard.