Creating TF1 from TGraph

I have converted your program into a script which can be run interactively in root.

// TGraph to TF1
TGraph *g1;
double myfunc(double *xx, double *)
{
   return g1->Eval(xx[0]);
}

// Main function

void diego()
{
   // Opening data. Here energy and PAI cross section relative to Rutherford cross section is provided
   TTree *MyTree = new TTree("MyTree","MyTree");
   Double_t energy, crossSection;
   MyTree->ReadFile("data-Bichsel.txt","energy/D:crossSection/D");
   MyTree->SetBranchAddress("energy",&energy);
   MyTree->SetBranchAddress("crossSection",&crossSection);

   // Probability of energy deposition
   Int_t nn = MyTree->GetEntries(); // number of entries on .txt file
   const Int_t n = nn;
   TVectorD ene(n), Pn1(n), sigma(n), Sigma(n), SSigma(n);
   TVectorD dSigma_dE(n), dSigmaRuth_dE(n), dSigmaRuth(n);

   const Double_t beta_lorentz = 0.97;
   const Double_t betagamma = beta_lorentz/sqrt(1 - pow(beta_lorentz,2));
   const Double_t mc2 = 0.510998928*pow(10,6);
   const Double_t Emax = 2*mc2*pow(betagamma,2);
   const Double_t kr = 2.54955*pow(10,-19); // constant used in Rutherford cross-section (eV.cm2)

   for (int i=0; i<n; i++) {
      MyTree->GetEntry(i);
      ene(i) = energy;
      sigma(i) = crossSection;

      // Rutherford cross-section
      dSigmaRuth_dE(i) = kr/pow(beta_lorentz*ene(i),2)*(1 - pow(beta_lorentz,2)*ene(i)/Emax);

      // Converting inital cross section
      Sigma(i) = sigma(i)*dSigmaRuth_dE(i);
   }

   TCanvas *c1 = new TCanvas("c1","c1",800,600);
   c1->cd();
   g1 = new TGraph(ene,Sigma);
   TSpline3 *s1 = new TSpline3("interpolation1",g1);
   s1->Draw();
   Double_t emin = 9.203623;
   Double_t emax = 94867.336;
   gPad->SetLogx();gPad->SetLogy();
   TF1 *f1 = new TF1("f1",myfunc,emin,emax);
   Double_t area = f1->Integral(emin,emax);
   cout << " Area: " << area << endl;
}

it gives:

$ root diego.C
   -----------------------------------------------------------------
  | Welcome to ROOT 6.09/01                     http://root.cern.ch |
  |                                    (c) 1995-2016, The ROOT Team |
  | Built for macosx64                                              |
  | From heads/master@v6-09-01-1076-g95ad22c, Jan 19 2017, 10:27:10 |
  | Try '.help', '.demo', '.license', '.credits', '.quit'/'.q'      |
   -----------------------------------------------------------------

root [0] 
Processing diego.C...
 Area: 1.84579e-20
root [1] 

and the attached plot