Consider the following for the next items that follow:

Let $f(x)= \begin{cases}\frac{x-3}{|x-3|}+a ; & x<3 \\ a-b ; & x=3 \\ \frac{x-3}{|x-3|}+b ; & x>3\end{cases}$ and f(x) be continuous at x = 3.

What is the value of b?

Consider the following for the next items that follow:

Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$

What is $\displaystyle \int_0^\pi\left(\sin ^4 x+\cos ^4 x\right) d x$ equal to?

Consider the following for the next items that follow:

Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$

What is I equal to?

Consider the following for the next items that follow:

Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$

If the function f(x) is differentiable at x = 1, then what is the value of (a + b)?