# Chapter 5: Integrals - Section 5.4 - The Fundamental Theorem of Calculus - Exercises 5.4 - Page 286: 6

$$\frac{{105}}{4}$$

#### Work Step by Step

\eqalign{ & \int_{ - 2}^3 {\left( {{x^3} - 2x + 3} \right)} dx \cr & {\text{integrate by using }}\int_a^b {{x^n}} dx = \left( {\frac{{{x^{n + 1}}}}{{n + 1}}} \right)_a^b \cr & = \left( {\frac{{{x^4}}}{4} - {x^2} + 3x} \right)_{ - 2}^3 \cr & {\text{evaluating, we get:}} \cr & = \left( {\frac{{{{\left( 3 \right)}^4}}}{4} - {{\left( 3 \right)}^2} + 3\left( 3 \right)} \right) - \left( {\frac{{{{\left( { - 2} \right)}^4}}}{4} - {{\left( { - 2} \right)}^2} + 3\left( { - 2} \right)} \right) \cr & {\text{simplifying, we get:}} \cr & = \frac{{81}}{4} - \left( { - 6} \right) \cr & = \frac{{105}}{4} \cr}

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