How is Jesus’ teaching in the Sermon on the Mount a “new law”

Below is a link to a video to watch to help answer the questions
https://m.youtube.com/watch?feature=related&v=BEGrTojD5vE

Question 1 : How is Jesus’ teaching in the Sermon on the Mount a “new law” for those who call themselves citizens of God’s Kingdom? Or is Jesus’ teaching not really “law” at all?

Question 2 :What one question arises for you from our materials this week?

Question 3: Pick one and only one of the following issues discussed in the Sermon on the Mount in Chapters 5 & 6 and describe how this issue has impacted your life.
Anger/Murder
Lust/Adultery
Divorce/Marital Fidelity
Honest Speech
Retaliation
Love for Enemies
Charity/Generosity
Prayer/Fasting
Treasures/Serving Two Masters
Worry
Describe the specific way the issue you choose has affected or impacted your life and then explain how Jesus’ teachings trouble, affirm, bless, or confuse you.