RooRealVar x{"x", "x", 0., 10.};
x.setBins(5); // five bins of width 2: edges at 0, 2, 4, 6, 8, 10

const double heights[5] = {1.0, 3.0, 2.0, 4.0, 1.5};

RooDataHist dh{"dh", "", x};
for (int i = 0; i < 5; ++i) {
   dh.set(i, heights[i], 0.0);
}

// The sub-range [3, 7] deliberately cuts through the bins [2,4] and [6,8].
x.setRange("partial", 3.0, 7.0);

const double binWidth = 2.0;
const double expected = (heights[1] * 1.0 + heights[2] * 2.0 + heights[3] * 1.0) / binWidth; // = 5.5

RooHistPdf analytic{"analytic", "", x, dh, 0};

RooHistPdf numeric{"numeric", "", x, dh, 0};
numeric.forceNumInt(true);

std::unique_ptr<RooAbsReal> integAna{analytic.createIntegral(x, RooFit::Range("partial"))};
std::unique_ptr<RooAbsReal> integNum{numeric.createIntegral(x, RooFit::Range("partial"))};

const double valAna = integAna->getVal();
const double valNum = integNum->getVal();

std::cout << "\n=== integral over the sub-range [3, 7] ===" << std::endl;
std::cout << "  expected (by hand)      : " << expected << std::endl;
std::cout << "  analytic (RooHistPdf)   : " << valAna << std::endl;
std::cout << "  numeric  (RooBinIntegr.): " << valNum << std::endl;