Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ \log\left( \frac { 1 }{ x } -1 \right) dx } \)

Evaluate the integral as the limit of a sum: \(\int _{ 1 }^{ 2 }{ (2x+1) } dx\)

Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ (x+4) } \)dx

Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ { x }^{ 2 } } dx\)

Evaluate the following integrals:
\(\int _{ 0 }^{ 3 }{ \frac { xdx }{ \sqrt { x+1 } +\sqrt { 5x+1 } } } \)