Question

Function f is continuous on the interval [-5,5] and the definite integral of f(x)dx from 0 to 5 is 4. What is the integral of f(x+2)dx from -2 to 3

Answer 1

I figured to set u=x+2 but I don't know what to do after that.

Answer 2

\[\int_0^5 f(x)~dx=4\]
Note that \(f(x+2)\) is \(f(x)\) shifted to the left by 2 units. If you did the same to the interval, you'd get \([0-2,5-2]\), or \([-2,3]\), which means
\[\int_0^5 f(x)~dx=\int_{-2}^3f(x+2)~dx=4\]