Originally Posted by
Krizalid Nasty, but possible.
Let's find where these curves intersect:
$\displaystyle f(x)=g(x)\implies x^2-19x+35=0.$
So we need to integrate a certain function on the interval $\displaystyle \left[ {\frac{{19 - \sqrt {221} }}
{2},\frac{{19 + \sqrt {221} }}
{2}} \right].$ The thing is, that in such interval $\displaystyle f(x)<g(x),$ then the integral to compute is
$\displaystyle \int_b^a {\left( {38x - 2x^2 - 70} \right)\,dx},$
where $\displaystyle \left[ {a,b} \right] = \left[ {\frac{{19 + \sqrt {221} }}
{2},\frac{{19 - \sqrt {221} }}
{2}} \right].$