If the area of the larger portion bounded between the curves $x^2+y^2=25$ and $y=|x-1|$ is $\frac{1}{4}(b \pi+c)$,where $b, c \in N$,then $b+c$ is equal to $ . . .. .. $

Let $A$ be the area of the region $\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2x(1-x)\}$. Then $540A$ is equal to

The area (in square units) of the region bounded by the curves $y + 2x^2 = 0$ and $y + 3x^2 = 1$ is equal to

The area bounded by the curves $y=x^2$ and $y-6=-|x|$ is

The area included between the parabolas $y^{2} = 5x$ and $x^{2} = 5y$ is

The following figure shows the graph of a continuous function $y=f(x)$ on the interval $[1,3]$. The points $A, B, C$ have coordinates $(1,1), (3,2), (2,3)$ respectively,and the lines $l_1$ and $l_2$ are parallel,with $l_1$ being tangent to the curve at $C$. If the area under the graph of $y=f(x)$ from $x=1$ to $x=3$ is $4$ sq units,then the area of the shaded region is