$\int_{a-c}^{b-c} f(x+c) \, dx = $

$\int_{-1}^2 |x| \, dx =$

If ${I_1} = \int_0^1 {2^{x^2}} dx$,${I_2} = \int_0^1 {2^{x^3}} dx$,${I_3} = \int_1^2 {2^{x^2}} dx$,and ${I_4} = \int_1^2 {2^{x^3}} dx$,then which of the following is true?

$\int_1^5 (|x-3| + |1-x|) \, dx =$

The value of $\int_1^5 (|x - 3| + |1 - x|) \, dx$ is

Let $f: R \rightarrow R$ be defined as $f(x)=e^{-x} \sin x$. If $F :[0,1] \rightarrow R$ is a differentiable function such that $F(x)=\int_{0}^{x} f(t) dt$,then the value of $\int_{0}^{1}(F'(x)+f(x)) e^{x} dx$ lies in the interval