-1

1

$$\pi$$  

$$\frac{\pi}{2}$$  

9

15

16

14

$$\frac{89}{6}$$  

$$\frac{23}{6}$$  

7

0

2.5

$$-\frac{5}{2}$$  

$$\frac{2}{5}$$  

$$-0.4$$  

2

$$-\frac{1}{2}$$  

$$-2$$  

$$0.5$$  

52

$$25$$  

$$-5\frac{2}{5}$$  

$$\frac{5}{2}$$  

antiderivative

indefinite integral

definite integral

derivative

calculating the area under a curve

$$\int_a^b\ f\left(x\right)\ dx=F\left(b\right)-F\left(a\right)$$

integrating a function, with no +C

using rectangles to approximate the area under a curve

we didn't learn this!

$$\int_b^af\left(x\right)\ dx=-\int_a^bf\left(x\right)\ dx$$  

$$\int_a^af\left(x\right)\ dx=0$$  

$$\int_a^bf\left(x\right)\ dx+\int_b^cf\left(x\right)\ dx$$  
$$=\int_a^cf\left(x\right)\ dx$$  

$$\int_a^bf\left(x\right)\ dx-\int_b^cg\left(x\right)\ dx$$  
$$=\int_a^c\left(f\left(x\right)-g\left(x\right)\right)\ dx$$  

$$\int_a^bf\left(x\right)\ dx-\int_a^bg\left(x\right)\ dx$$  
$$=\int_a^b\left(f\left(x\right)-g\left(x\right)\right)\ dx$$