To solve dis elliptic integral

I need to solve dis eqn

x= alpha*((sin(theta1)*(int(sin(phi)/(sqrt(a+(b*sin(phi)))))))+ (cos(theta1)*(int(cos(phi)/(sqrt(a+(b*sin(phi))))))))

In this eqn,

phi=theta1+theta;

where theta1 is known,

a and b are known,

[Walter Roberson]

What are the limits for the integration? What is the variable of integration?