Evaluate the following integrals as limit of sum: `int_1^3(3x^2+1)dx`

Explanation

`\int_{1}^{3}(3 x^{2}+1) d x`
`=\lim _{h \rightarrow 0} h[3 h^{2}(1^{2}+2^{2}+\ldots+(n-1)^{2}).`
`+6 h(1+2+\ldots+(n-1))+4n`
`=\lim _{h \rightarrow 0}[\frac{3(n h-h)(n h)(2 n h-h)}{6}.`
`=\lim _{h \rightarrow 0}[\frac{3(2-h) \cdot 2 \cdot(4-h)}{6}+\frac{6(2-h) \cdot 2}{2}+8]`
`=8+12+8=28`