If a curve \( y=f(x) \) passes through the point \( (1,2) \) and satisfies \( x \frac{d y}{d x}+y=b x^{4} \), then for w…

If a curve \( y=f(x) \) passes through the point \( (1,2) \) and satisfies \( x \frac{d y}{d x}+y=b x^{4} \), then for what value of \( b \), \( \int_{1}^{2} f(x) d x=\frac{62}{5} ? \)

[JEE Main 2021, 24 Feb (Shift 2)]