Evaluate: \(\int _{ 0 }^{ 3 }{ (3{ x }^{ 2 }-4x+5) } dx\)

Evaluate :\(\int _{ 0 }^{ 1 }{ [2x] } dx\) where [⋅] is the greatest integer function

Evaluate the following \(\int _{ 0 }^{ \pi /2 }{ { cos}^{ 7}x\quad dx } \)

Evaluate the following
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }x{ cos }^{ 4 }xdx } \)

Find the area bounded by y=x²+2,x-x-axis, x=1 and x=2