Let Px=x2+bx+c be a quadratic polynomial with real coefficients such that ∫01Pxdx=1 and Px  leaves remainder 5 when it is divided by x−2. Then the value of  is 9b+c equal to

∫01x2+bx+cdx=1x33+bx22+cx01=113+b2+c=13b+6c=5                               ...... (1)Given the remianinder when P(x)  is divided by (x-2) is 5It means P(2) =54+2b+c=583+4b2+2c=52b+c=1                             ......(2)  Solving  b=29,c=59,b+c=79,9(b+c)=7