We can approximate via trapezoid rule for the function is continous.

In order to use the trapezoid rule tou need to find the number of intervals.

In this case the length is 2.6-1=1.6

Then divided by the length of each one 1.6/.4=4

Thus, a use of 4 intervals.

By the trapezoid rule we need to find,

f(1),f(1.4),f(1.8),f(2.2),f(2.6)

We note that,

f(1)=(1)^2*sin(1)=0.84

f(1.4)=(1.4)^2*sin(1.4)=1.93

f(1.8)=(1.8)^2*sin(1.8)=3.16

f(2.2)=(2.2)^2*sin(2.2)=3.91

f(2.6)=(2.6)^2*sin(2.6)=3.48

Now we double the inner terms (look at formula)

Thus,

f(1)=.84

2f(1.4)=3.86

2f(1.8)=7.32

2f(2.2)=7.82

f(2.6)=3.48

Add them together,

Result=23.32

Now multiply it by the length of each interval, (.4)

Thus,

9.33

Finally multiply by 1/2,

4.67

That is the approximate answer.