Evaluate the following definite integrals as limit of sum: `int_1^4(x^2+x)dx`

Explanation

Let `I=int^{4}(x^{2}+x) d x`


`=int_{4}^{4} x^{2} d x+int^{4} x d x`


Let `I=I_{1}+I_{2}`, where `I_{1}=int^{1} x^{2} d x` & `I_{2}=int^{1} x d x`

We know that,


`int_{a}^{b} f(x) d x=(b-a) lim _{n rightarrow infty} frac{1}{n}[f(a)+f(a+h)+f(a+(n-1) h)]`
where , `h=frac{b-a}{n}`


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