`int_0^4(x^2)/(x+1)dx=?`

int_0^1(x^2)/(1+x^2)dx=?

int_0^1(x^2-2)/(x^2+1)dx=?

int_0^2(3x^2+4x-5)dx=?

int_0^3(4x^3+2x-3)dx=?

If P=int_0^oo(x^2)/(1+x^4)dx ; Q=int_0^oo(x dx)/(1+x^4)"and"R=int_0^oo(dx)/(1+x^4), then prove that :

int_0^1 (x+x^2)dx

Evaluate: int_0^1log(x^2+x+1)dx

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=