According to the will of Alfred Nobel, he did not establish an award for Mathematics because he felt that mathematics did not have a significant impact on science. He felt that chemistry, medicine, physics, peace and literature highly influenced science and global populations. There was already a prestigious mathematical award at that time awarded by Swedish Monarch Oscar II. Alfred Nobel didn’t want to compete with the king.
Mathematics was left out because he couldn’t see a direct impact of it on science. It must be noted that integrals seem more interesting and useful when you know that it represents area under a curve and might appear inconsequential if not applied or coupled with hard sciences discussed earlier. For this reason he didn’t feel the need to award mathematicians with a prize.
I don’t blame Alfred Nobel for doing so because the guy was pretty much giving away his own money. He can give it to anyone he wants. His gesture was far greater than that of most people. So it is not a big deal if he didn’t feel the need to give his money to high achievers of a particular field.