Question

Draw pictures illustrating the fact that if $a\le c\le b$then

${\int }_a^{c}f\left(x\right)dx+{\int }_c^{b}f\left(x\right)dx={\int }_a^{b}f\left(x\right)dx$

Short answer

The graphs are as follows

Step-by-step solution

Step 1. Given information

An identity is given as${\int }_a^{c}f\left(x\right)dx+{\int }_c^{b}f\left(x\right)dx={\int }_a^{b}f\left(x\right)dx$

Step 2. Graphs 

Draw the of individual functions and then compare them.

The first graph of $f\left(x\right)=x^2\&from0\to 0.5$

Now the second graph of $f\left(x\right)=x^2\&from0.5\to 1$

Last graph of $f\left(x\right)=x^2\&from0\to 1$

From the above graphs we can conclude that

${\int }_a^{c}f\left(x\right)dx+{\int }_c^{b}f\left(x\right)dx={\int }_a^{b}f\left(x\right)dx$