People who observes this world as science depicts should overwhelm about their claim because they can't prove it as science can. As science can't prove all matters with solid proof but people's rationality makes it guessable so why the questions and answers received world wide and human beings using those with honor.
But no prophets tried their best to proof all they are claiming they just practice on their life and some miracles help them to establish facts as their will and claiming those issues as the help from Allah. Yet people feel they fully occupied with so much uncertenities to consider and solve they have nothing but rely on religious sayings. But hard part of Islam is people's faith should be examined by harsh reality, such as when you are in difficulties and you know the solution some worldly methods can do but wait for Allah to help and firm faith about your wrong doings will put you in hell as well as boost that problem after some time.
Your obidiance on prophets and rules they practiced in daily live is the easier answer but the hard part of this is not guessable easily. Some rationality will not allow you to believe that they did the best and you should follow him with out questions, after some experiences harsh reality comes in believing them as you believe your eyes or ears as well as your reasoning could be wrong but prophets actions are right and trustworthy.