The slope to the curve y = f(x) at (x, f(x)) is 2x + 1. If the curve passes through the point (1, 2), then the area of the region bounded by the curve y = f(x), the x-axis and the line x = 1 is

5/6

We are given that $\frac{dy}{dx}=2x+1$

⇒ y = x² + x + c, and since the curve passes through the point (1, 2), c = 0.

Hence the curve is y = x² + x (see the figure); the required area $=\int\limits_0^1y\,dx=\int\limits_0^1(x^2+x)dx=\frac{5}{5}$.

Hence (A) is the correct answer.