The numbers $A, B$ and C such that a function of the form $f \left(x\right) = A x2 + Bx + C$satisfies the conditions

$f^{\mathrm{\prime }}\left(1\right)=8,f\left(2\right)+f^{\prime \prime }\left(2\right)=33$ and ${\int }_0^1 f\left(x\right)\mathrm{d}x=7/3$ are

• A

  $A = 1, B = – 4, C = 2$

• B

  $A=7,B=–6, C=3$

• C

  $A=8,B=-6,C=3$

• D

  none of these.