NProbability[x > 1, x \[Distributed] NormalDistribution[]]

NProbability[x > 1, x \[Distributed] NormalDistribution[], Method->"MonteCarlo"]

NExpectation[x Sin[x] + 1, x \[Distributed] NormalDistribution[]]

NExpectation[x Sin[x] + 1, x \[Distributed] NormalDistribution[], Method->"MonteCarlo"]