How to use android canvas to draw a Rectangle with only topleft and topright corners round?

Use a path. It has the advantage of working for APIs less than 21 (Arc is also limited thusly, which is why I quad). Which is a problem because not everybody has Lollipop yet. You can however specify a RectF and set the values with that and use arc back to API 1, but then you wouldn't get to use a static (without declaring a new object to build the object).

Drawing a rounded rect:

    path.moveTo(right, top + ry);
    path.rQuadTo(0, -ry, -rx, -ry);
    path.rLineTo(-(width - (2 * rx)), 0);
    path.rQuadTo(-rx, 0, -rx, ry);
    path.rLineTo(0, (height - (2 * ry)));
    path.rQuadTo(0, ry, rx, ry);
    path.rLineTo((width - (2 * rx)), 0);
    path.rQuadTo(rx, 0, rx, -ry);
    path.rLineTo(0, -(height - (2 * ry)));
    path.close();

As a full function:

static public Path RoundedRect(float left, float top, float right, float bottom, float rx, float ry, boolean conformToOriginalPost) {
    Path path = new Path();
    if (rx < 0) rx = 0;
    if (ry < 0) ry = 0;
    float width = right - left;
    float height = bottom - top;
    if (rx > width/2) rx = width/2;
    if (ry > height/2) ry = height/2;
    float widthMinusCorners = (width - (2 * rx));
    float heightMinusCorners = (height - (2 * ry));

    path.moveTo(right, top + ry);
    path.rQuadTo(0, -ry, -rx, -ry);//top-right corner
    path.rLineTo(-widthMinusCorners, 0);
    path.rQuadTo(-rx, 0, -rx, ry); //top-left corner
    path.rLineTo(0, heightMinusCorners);

    if (conformToOriginalPost) {
        path.rLineTo(0, ry);
        path.rLineTo(width, 0);
        path.rLineTo(0, -ry);
    }
    else {
        path.rQuadTo(0, ry, rx, ry);//bottom-left corner
        path.rLineTo(widthMinusCorners, 0);
        path.rQuadTo(rx, 0, rx, -ry); //bottom-right corner
    }

    path.rLineTo(0, -heightMinusCorners);

    path.close();//Given close, last lineto can be removed.

    return path;
}

You'd want to line all the way to those corner bits, rather than quad across them. This is what setting true to conformToOriginalPost does. Just line to the control point there.

If you want to do that all but don't care about pre-Lollipop stuff, and urgently insist that if your rx and ry are high enough, it should draw a circle.

@TargetApi(Build.VERSION_CODES.LOLLIPOP)
static public Path RoundedRect(float left, float top, float right, float bottom, float rx, float ry, boolean conformToOriginalPost) {
    Path path = new Path();
    if (rx < 0) rx = 0;
    if (ry < 0) ry = 0;
    float width = right - left;
    float height = bottom - top;
    if (rx > width/2) rx = width/2;
    if (ry > height/2) ry = height/2;
    float widthMinusCorners = (width - (2 * rx));
    float heightMinusCorners = (height - (2 * ry));

    path.moveTo(right, top + ry);
    path.arcTo(right - 2*rx, top, right, top + 2*ry, 0, -90, false); //top-right-corner
    path.rLineTo(-widthMinusCorners, 0);
    path.arcTo(left, top, left + 2*rx, top + 2*ry, 270, -90, false);//top-left corner.
    path.rLineTo(0, heightMinusCorners);
    if (conformToOriginalPost) {
        path.rLineTo(0, ry);
        path.rLineTo(width, 0);
        path.rLineTo(0, -ry);
    }
    else {
        path.arcTo(left, bottom - 2 * ry, left + 2 * rx, bottom, 180, -90, false); //bottom-left corner
        path.rLineTo(widthMinusCorners, 0);
        path.arcTo(right - 2 * rx, bottom - 2 * ry, right, bottom, 90, -90, false); //bottom-right corner
    }

    path.rLineTo(0, -heightMinusCorners);

    path.close();//Given close, last lineto can be removed.
    return path;
}

So, conformToOriginalPost actually draws a rounded rect without the bottom two bits rounded.

I would draw two rectangles:

canvas.drawRect(new RectF(0, 110, 100, 290), paint);
canvas.drawRoundRect(new RectF(0, 100, 100, 200), 6, 6, paint);

Or something like that, you just overlap them so that the upper corners will be round. Preferably you should write a method for this