By a) Trapezoidal rule

b) simpsons 1/3rd rule.

Using following table

Let $a=0$ and $b=6 $

Here $h=1$ and $n=6 $

Let $y=g(x)=xf(x)$

1) Trapezoidal rule

$\int\limits_a^b g(x) dx=\dfrac h2[(y_0+y_6)+2(y_1+y_2+y_3+y_4+y_5)]\\ =\dfrac 12[(0+1.38)+2(0.161+0.352+0.57+0.816+1.08+1.38)]\\ =\dfrac 12[1.38+2(2.984)]\\ =3.674$

2) Simpsons 1/3rd rule

$\int\limits_a^b g(x) dx=\dfrac h2[(y_0+y_6)+4(y_1+y_3+y_5)+2(y_2+y_4)]\\ =\dfrac 13[(0+1.38)+4(0.161+0.57+1.085)+2(0.816+0.352)]\\ =\dfrac 13[1.38+4(1.816)+2(1.168)]\\ =3.66$