Question
If $\displaystyle\int_0^1 \frac{x^4(1-x)^4}{1+x^2} \, dx = \frac{22}{7} - \pi$, find the value of $7\displaystyle\int_0^1 \frac{x^4(1-x)^4}{1+x^2} \, dx + 7\pi$ rounded to the nearest integer.
If $\displaystyle\int_0^1 \frac{x^4(1-x)^4}{1+x^2} \, dx = \frac{22}{7} - \pi$, find the value of $7\displaystyle\int_0^1 \frac{x^4(1-x)^4}{1+x^2} \, dx + 7\pi$ rounded to the nearest integer.