HELP PLEASE WITH INTEGRALS:(?

Question

g(x)=∫ 0 to x (upper is x and lower is 0) t^3+1dt
g(x)=∫0 to x^2 t+1dt
g(x)= ∫0 to x^2 e^sint dt
g(x)=∫x to 2x+1 t+1dt

Answer 1

Rational functions:

Therefore 

Answer 2

2). 

Rational functions: 

.

Answer 3

4).

Rational functions:

Answer 4

The function is .

The power series of .

The second degree power series of .

Consider