I'm guessing the sum is
[tex]\displaystyle\lim_{n\to\infty}\sum_{i=1}^nx_i\ln(1+{x_i}^2)\Delta x[/tex]
Comparing to the definition of the definite integral, this limit quite clearly corresponds to the definite integral
[tex]\displaystyle\int_0^3x\ln(1+x^2)\,\mathrm dx[/tex]
