Question 302713
You didn't specify a method. 
Break up the area into 5 regions.
Calculate an average value of f(x) and the right and left endpoint. 
Then multiply the average value of f(x) by dx in each region. 
{{{ x=0}}}, {{{ f(0)=4.25}}}
{{{ x=1}}}, {{{ f(1)=7.25}}}
{{{ x=2}}}, {{{ f(2)=8.25}}}
{{{ x=3}}}, {{{ f(3)=7.25}}}
{{{ x=4}}}, {{{ f(4)=4.25}}}
{{{ x=5}}}, {{{ f(5)=-0.75}}}
SO then area 1 equals,
{{{A1=(1/2)(f(0)+f(1))*(1-0)=5.75 }}}
{{{A2=(1/2)(f(1)+f(2))*(2-1)=7.75}}}
{{{A3=(1/2)(f(2)+f(3))*(3-2)=7.75}}}
{{{A4=(1/2)(f(3)+f(4))*(4-3)=5.75}}}
{{{A5=(1/2)(f(4)+f(5))*(5-4)=1.75}}}
{{{Atot=A1+A2+A3+A4+A5=28.75}}}
The exact value is {{{29.583}}} so that's a pretty good approximation (within 3%).