mathematical transition of an integral

YouTube - Module 1_5_7 | MIT 8.02SC Physics II: Electricity and Magnetism, Fall 2010

(this posted has latex errors i dont know why)

here is a print screen of the post

http://i54.tinypic.com/2zi0kex.jpg

in here in the end

i got an arch that startes at A and end in B

he wrote this integral

but point a and be are not values that i can put in

if my function depends on "r" then i need to change dl to be dr expression somehow

?

i think that the integral should go from 0 to pi

and dl should be d theta expression (instead of dr)

and dl =r*d(theta)

R is constant

i get

i get 2pi/R

this resolt is different from the resolt he gets

why?