ccl:the intergral over heat capacities



Hello CCLers,
 I have been looking at this problem for some time. I think I am too close to
 the problem to see the answer.
 I would therefore like some help please.
 Let me quote from a paper
 "The C-H Bond Energy of Benzene" J.Am. Chem. Soc. vol 117, No.9, 1995
 page
 2595
 ..... The heat of formation for c6h6 at zero K can be estimated if one knows
 the heat capacities of benzene, C atom, and H2.
 Delta f H298(C6H6) = Delta f H0(C6H6) + intergral between 0 and 298 dT[
 Cp(C6H6) - 6Cp(C) - 3Cp(h2)]
 In the equation above the intergral over the heat capacities is evaluated as
 [+3.407 - 7.578] = -4.2 kcal mol-1.
 end of quote
 I have been trying to work out how the writers (Davico, Bierbaum, Depuy,
 Ellison and Squires) used this equation to arrive at the value for the
 intergal over the heat capacities as - 4.2 kcal mol-1.
 Any help would be extremely welcome. Thanks and am sorry as this seems to be
 a simple task though a can not see the wood for the trees.
 Ian