how to calculate integral?
That depends which integral.
I'll do a very simple one for you.
$$\int 5x^6+\frac{9}{2}x^3 +4 \;dx\\\\ =\frac{5x^{6+1}}{7}+\frac{9x^{3+1}}{2\times4}+4x+c\\\\ =\frac{5x^{7}}{7}+\frac{9x^{4}}{8}+4x+c\\\\$$