Let P (x)=x^2+ b x+ c be a quadratic polynomial with real coefficients such that ∫_0^1 P (x) d x=1 and P (x) leaves remainder 5 when it is divided by…

Let $\displaystyle \mathrm{P}(x)=x^2+\mathrm{b} x+\mathrm{c}$ be a quadratic polynomial with real coefficients such that $\displaystyle \int_0^1 \mathrm{P}(x) \mathrm{d} x=1$ and $\displaystyle \mathrm{P}(x)$ leaves remainder $\displaystyle 5$ when it is divided by ( $\displaystyle x-2$ ). Then the value of $\displaystyle 9(\mathrm{~b}+\mathrm{c})$ is equal to :