The indefinite integral $I=\int \frac{{\left({\sin }^{2}x-{\cos }^{2}x\right)}^{2019}}{{\left(\sin x\right)}^{2021}{\left(\cos x\right)}^{2021}}dx$ simplifies to (where $c$ is an integration constant)

• A

  $\frac{{\left({\sin }^{2}x-{\cos }^{2}x\right)}^{2020}}{2020}+c$
• Correct answer
  B

  $\frac{{\left(\tan x-\cot x\right)}^{2020}}{2020}+c$
• C

  $\frac{{\left(\sin x-\cos x\right)}^{2020}}{2020}+c$
• D

  $\frac{{\left({\tan }^{2}x+{\cot }^{2}x\right)}^{2020}}{2020}+c$

Hence, the correct answer is option: 'B'.