1. $int_{1}^{2}(3x^{2}-2x + 1)dx$

Answer:

$4$

Explanation:

Step1: Find the antiderivative

$\int(3x^{2}-2x + 1)dx=x^{3}-x^{2}+x+C$

Step2: Apply the fundamental theorem of calculus

$\left[x^{3}-x^{2}+x\right]_1^2=(2^{3}-2^{2}+2)-(1^{3}-1^{2}+1)$

Step3: Calculate the values

$(8 - 4+2)-(1 - 1+1)=6 - 1=4$