Evaluate the following integral as the limit of sum:

${\int }_0^2(x+4)dx$.

Evaluate the following integral as the limit of sum:

${\int }_1^2(3x-2)dx$

Evaluate the ${\int }_1^3{x}^{2}dx$ as the limit of sum.

Evaluate ${\int }_0^3\left(x^2+1\right)dx$ as the limit of sum.

Evaluate ${\int }_2^5\left(3x^2-5\right)dx$ as the limit of sum.

Evaluate ${\int }_0^3\left(x^2+2x\right)dx$ as the limit of sum.

Evaluate ${\int }_1^4\left(3x^2+2x\right)dx$ as the limit of sum.

Evaluate ${\int }_1^3\left(x^2+5x\right)dx$ as the limit of sum.

Evaluate the following integral as the limit of sum:

${\int }_1^3\left(2x^2+5x\right)dx$