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

\(\frac{5}{6}\)

\(\frac{dy}{dx} = 2x + 1\)

⇒ ∫dy = ∫(2x + 1) dx 

y = x² + x + c

It passes through (1,2) ⇒ c = 0, then curve is y = x² + x

The area bounded by y = x² + x, x - axis and line x = 1 is : 

\(\int_{0}^{1} [x^2 + x] dx = \frac{5}{6}\)