Suppose we are given two curves represented by y=f(x),y=g(x) where $f(x)\geq g(x)$ in [a,b].

Here the points of intersection of these two curves are given by x=a and y=b obtained by taking common values of y from the given equation of two curves.

Hence dA=[f(x)-g(x)]dx and the total area A can be taken as $A=\int_a^b[f(x)-g(x)]dx$.

Given two curves f(x)=x and g(x)=$x^2$.

To find the limits,let us find the points of interaction of the curves.

since y=x and y=x^2

on equating we get x=$x^2$

$(x^2-x)=0$

x(x-1)=0

x=0 or x=1

Hence the points of intersection are (0,0) and(1,1)

Hence,the limits can be taken as x=0 and x=1

Now the required area can be found by using the information in the tool box:

$A=\int_a^b[f(x)-g(x)dx]$

Here a=0,b=1 f(x)=x and $g(x)=x^2$

Therefore \begin{array}{1 1}A=\int_0^1[x-x^2]dx \\ =\begin{bmatrix}\frac{x^2}{2}-\frac{x^3}{3}\end{bmatrix}_0^1\\=\frac{1}{6}sq.units\end{array}

Hence the required area is $\frac{1}{6}$sq.units.