one - a - day multi vitamins #5\n5 - 4 - 3 - 2 - 1\n5 multiple choice: do one - a - day!\n1…

Explanation:

Step1: Find the antiderivative

Use the power rule for integration (\int x^n dx=\frac{x^{n + 1}}{n+1}+C) ((n\neq - 1)). For (\int(4x^{3}-6x)dx), we have: (\int(4x^{3}-6x)dx=4\int x^{3}dx-6\int xdx) (=4\times\frac{x^{4}}{4}-6\times\frac{x^{2}}{2}+C=x^{4}-3x^{2}+C)

Step2: Apply the fundamental theorem of calculus

The fundamental theorem of calculus states that (\int_{a}^{b}f(x)dx=F(b)-F(a)), where (F(x)) is the antiderivative of (f(x)). Here (a = 1), (b = 2), and (F(x)=x^{4}-3x^{2}) (F(2)-F(1)=(2^{4}-3\times2^{2})-(1^{4}-3\times1^{2})) First, calculate (2^{4}-3\times2^{2}): (2^{4}-3\times2^{2}=16 - 12=4) Then, calculate (1^{4}-3\times1^{2}): (1^{4}-3\times1^{2}=1 - 3=-2) Now, (F(2)-F(1)=4-(-2))

Step3: Simplify the result

(4-(-2)=4 + 2=6)

Answer:

C. 6