The curve \(y=ax^2+bx+c\) passes through the points \((1,0)\) and \((2,0)\) and its gradient at the point \((2,0)\) is \(2\). Find the numerical value of the area included between the curve and the axis of \(x\).

The curve \(y=ax^2+bx+c\) passes through the points \((1,0)\) and \((2,0)\) and its gradient at the point \((2,0)\) is \(2\). Find the numerical value of the area included between the curve and the axis of \(x\).