f(x)=√2sin(x-π/4)+b
π/2+2kπ& lt； = x-π/4 & lt； =3π/2+2kπ，k∈Z
π/4+2kπ& lt； = x & lt=5π/4+2kπ，k∈Z
∴ Monotone decreasing interval [π/4+2kπ, 5π/4+2kπ], k∈Z
(2)
∫x∈[0，π]
∴x-π/4∈[-π/4,3π/4]
∴sin(x-π/4)∈[-√2/2, 1]
A & lt0
∴√2asin(x-π/4)∈[√2a,-a]
∴f(x)∈[√2a+a+b,b]
* The range is [2,3]
∴b=3
√2a+a+b=2
a =- 1/( 1+√2)= 1-√2。
Hope to adopt ~ thank you.