Learning Target FTC$3*-$ Section $5\mathrm{.}2$ I can evaluate definite integrals exactly by using the properties of definite integrals, graphs and geometry.

Criteria for $$ grade:

All calculus work is done correctly. Sufficient work shown. Use exact answers, not decimal approximations.

Uses calculus to arrive at the answer, not graphical or numerical estimates or guesses.

One or two small arithmetic mistakes may be accepted if it does not significantly alter the problem's intent.

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Formulas for Areas of Shapes

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The graph of the continuous function $f(x)$ is given below. Use geometry to answer the following.

a$.$ In the graph of $f(x)$ given below, shade the region whose area is equal to the following integral ${\displaystyle \underset{-3}{\overset{8}{}}}f(x)dx.$

b$.$ Use formulas for the areas of shapes to evaluate the definite integral ${\displaystyle \underset{-3}{\overset{8}{}}}f(x)dx.$

Suppose ${\displaystyle \underset{6}{\overset{11}{}}}h(x)dx=9,{\displaystyle \underset{-2}{\overset{11}{}}}f(x)dx=-2,$ and ${\displaystyle \underset{-2}{\overset{6}{}}}f(x)dx=7.$ Find the value of ${\displaystyle \underset{6}{\overset{11}{}}}(3h(x)-5f(x))dx.$

Please help with graph as well.