Find ${\displaystyle \underset{1}{\overset{4}{}}}(x^2-3x)dx$ using the Evaluation Theorem $($ie anti$-$derivatives$)$

If $f(x)=x^2-3x,$ clearly define what $F(x)$ is$.$

Do we need to add a $\text{'}+$C $\text{'}$ in taking the anti$-$derivative in this case?

Explain why or why not.

Using words, interpret the value of the Definite Integral you got in the context of this function $f(x).$

Find ${\displaystyle \underset{1}{\overset{4}{}}}(x^2-3x)dx$ using the Evaluation Theorem $($ie anti$-$derivatives$)$

If $f(x)=x^2-3x,$ clearly define what $F(x)$ is$.$

Do we need to add a $\text{'}+$C $\text{'}$ in taking the anti$-$derivative in this case?

Explain why or why not.

Using words, interpret the value of the Definite Integral you got in the context of this function $f(x).$

PLEASE SHOW ALL STEPS