I don't remember that calculus stuff very well, but since no one's 
helped you yet, me and my pocket calculator had a go at it:

volume:
  a:=2*int( sqrt(r^2-(x-R)^2) ,x,0,R+r )  // 1/2 torus cross-section
  int( a*R,theta,0,2*pi )                 // object of revolution
> R*pi*( pi*r*abs(r)+2*R*sqrt(r^2-R^2)+2*pi*asin(R*abs(1/r))/180*r^2 )

Odds are this is wrong.. Not sure about line 2.

area:
  c:=2*sin(R/r)*r 			// part of arc inside torus
  int( (2*pi*r-c)*R ,theta,0,2*pi )
> -4*r*R*pi*(sin(R/r)-pi)

or something

sig.


David Fontaine wrote:
> 
> What are the equations for surface area and volume of a torus,
> *including* torii with minor>major radius?
> 
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